Here is is:

Feb  4 22:19:00 hppb kernel: [ 7615.521927] usb 3-3: new high-speed USB device number 8 using xhci_hcd
Feb  4 22:19:00 hppb kernel: [ 7615.541705] usb 3-3: New USB device found, idVendor=1bcf, idProduct=0c31
Feb  4 22:19:00 hppb kernel: [ 7615.541709] usb 3-3: New USB device strings: Mfr=1, Product=2, SerialNumber=3
Feb  4 22:19:00 hppb kernel: [ 7615.541711] usb 3-3: Product: USB to Serial-ATA bridge
Feb  4 22:19:00 hppb kernel: [ 7615.541713] usb 3-3: Manufacturer: Sunplus Innovation Technology 
Feb  4 22:19:00 hppb kernel: [ 7615.541714] usb 3-3: SerialNumber: FDC0FD10EA00000FD0FCAF55667939
Feb  4 22:19:00 hppb kernel: [ 7615.543532] usbip-host 3-3:1.0: 3-3 is not in match_busid table... skip!
Feb  4 22:19:00 hppb kernel: [ 7615.543550] usb-storage 3-3:1.0: USB Mass Storage device detected
Feb  4 22:19:00 hppb kernel: [ 7615.543607] scsi7 : usb-storage 3-3:1.0
Feb  4 22:19:00 hppb mtp-probe: checking bus 3, device 8: "/sys/devices/pci0000:00/0000:00:14.0/usb3/3-3"
Feb  4 22:19:00 hppb mtp-probe: bus: 3, device: 8 was not an MTP device
Feb  4 22:19:00 hppb laptop-mode: Laptop mode 
Feb  4 22:19:00 hppb laptop-mode: enabled, not active
Feb  4 22:19:00 hppb laptop-mode: Laptop mode 
Feb  4 22:19:00 hppb laptop-mode: enabled, not active
Feb  4 22:19:01 hppb kernel: [ 7616.548233] scsi 7:0:0:0: Direct-Access     WDC WD10 EADS-11M2B1      0200 PQ: 0 ANSI: 4
Feb  4 22:19:01 hppb kernel: [ 7616.548469] sd 7:0:0:0: Attached scsi generic sg2 type 0
Feb  4 22:19:01 hppb kernel: [ 7616.549535] sd 7:0:0:0: [sdb] 1953525168 512-byte logical blocks: (1.00 TB/931 GiB)
Feb  4 22:19:01 hppb kernel: [ 7616.556319] sd 7:0:0:0: [sdb] Write Protect is off
Feb  4 22:19:01 hppb kernel: [ 7616.556323] sd 7:0:0:0: [sdb] Mode Sense: 38 00 00 00
Feb  4 22:19:01 hppb kernel: [ 7616.563195] sd 7:0:0:0: [sdb] No Caching mode page found
Feb  4 22:19:01 hppb kernel: [ 7616.563209] sd 7:0:0:0: [sdb] Assuming drive cache: write through
Feb  4 22:19:01 hppb kernel: [ 7616.577746] sd 7:0:0:0: [sdb] No Caching mode page found
Feb  4 22:19:01 hppb kernel: [ 7616.577760] sd 7:0:0:0: [sdb] Assuming drive cache: write through
Feb  4 22:19:01 hppb kernel: [ 7616.640281]  sdb: sdb1 sdb2
Feb  4 22:19:01 hppb kernel: [ 7616.655220] sd 7:0:0:0: [sdb] No Caching mode page found
Feb  4 22:19:01 hppb kernel: [ 7616.655225] sd 7:0:0:0: [sdb] Assuming drive cache: write through
Feb  4 22:19:01 hppb kernel: [ 7616.655228] sd 7:0:0:0: [sdb] Attached SCSI disk
Feb  4 22:19:01 hppb kernel: [ 7617.025578] btrfs: device label WDC-Green devid 1 transid 832 /dev/sdb1
Feb  4 22:19:01 hppb kernel: [ 7617.026076] btrfs: device label WDC-Green devid 2 transid 832 /dev/sdb2
Feb  4 22:19:01 hppb kernel: [ 7617.049763] btrfs: device label WDC-Green devid 1 transid 832 /dev/sdb1
Feb  4 22:19:01 hppb kernel: [ 7617.050255] btrfs: device label WDC-Green devid 2 transid 832 /dev/sdb2
Feb  4 22:19:01 hppb anacron[7182]: Anacron 2.3 started on 2015-02-04
Feb  4 22:19:01 hppb anacron[7183]: Anacron 2.3 started on 2015-02-04
Feb  4 22:19:01 hppb anacron[7183]: Job `1_Profilo_principale' locked by another anacron - skipping
Feb  4 22:19:01 hppb anacron[7182]: Will run job `1_Profilo_principale' in 0 min.
Feb  4 22:19:01 hppb anacron[7182]: Will run job `2_VirtualBox_VMs' in 0 min.
Feb  4 22:19:01 hppb anacron[7182]: Jobs will be executed sequentially
Feb  4 22:19:01 hppb anacron[7182]: Job `1_Profilo_principale' started
Feb  4 22:19:01 hppb anacron[7183]: Job `2_VirtualBox_VMs' locked by another anacron - skipping
Feb  4 22:19:01 hppb anacron[7183]: Normal exit (0 jobs run)
Feb  4 22:19:01 hppb anacron[7182]: Job `1_Profilo_principale' terminated
Feb  4 22:19:01 hppb anacron[7182]: Job `2_VirtualBox_VMs' started
Feb  4 22:19:01 hppb anacron[7182]: Job `2_VirtualBox_VMs' terminated
Feb  4 22:19:01 hppb anacron[7182]: Normal exit (2 jobs run)
Feb  4 22:19:01 hppb console-kit-daemon[2107]: GLib-CRITICAL: Source ID 91 was not found when attempting to remove it
Feb  4 22:19:01 hppb console-kit-daemon[2107]: GLib-CRITICAL: Source ID 94 was not found when attempting to remove it
Feb  4 22:19:01 hppb anacron[7220]: Anacron 2.3 started on 2015-02-04
Feb  4 22:19:01 hppb anacron[7220]: Normal exit (0 jobs run)
Feb  4 22:19:02 hppb anacron[7223]: Anacron 2.3 started on 2015-02-04
Feb  4 22:19:02 hppb anacron[7223]: Normal exit (0 jobs run)
Feb  4 22:19:02 hppb console-kit-daemon[2107]: GLib-CRITICAL: Source ID 114 was not found when attempting to remove it
Feb  4 22:19:02 hppb console-kit-daemon[2107]: GLib-CRITICAL: Source ID 111 was not found when attempting to remove it
Feb  4 22:19:02 hppb anacron[7257]: Anacron 2.3 started on 2015-02-04
Feb  4 22:19:02 hppb anacron[7259]: Anacron 2.3 started on 2015-02-04
Feb  4 22:19:02 hppb anacron[7257]: Will run job `1_Profilo_principale' in 0 min.
Feb  4 22:19:02 hppb anacron[7257]: Jobs will be executed sequentially
Feb  4 22:19:02 hppb anacron[7257]: Job `1_Profilo_principale' started
Feb  4 22:19:02 hppb anacron[7259]: Job `1_Profilo_principale' locked by another anacron - skipping
Feb  4 22:19:02 hppb anacron[7259]: Normal exit (0 jobs run)
Feb  4 22:19:02 hppb anacron[7257]: Job `1_Profilo_principale' terminated
Feb  4 22:19:02 hppb anacron[7257]: Normal exit (1 job run)
Feb  4 22:19:02 hppb console-kit-daemon[2107]: GLib-CRITICAL: Source ID 139 was not found when attempting to remove it
Feb  4 22:19:02 hppb console-kit-daemon[2107]: GLib-CRITICAL: Source ID 136 was not found when attempting to remove it
Feb  4 22:19:02 hppb backintime (mauro): INFO: Lock
Feb  4 22:19:02 hppb backintime (mauro): INFO: Lock
Feb  4 22:19:02 hppb backintime (root): INFO: Lock
Feb  4 22:19:02 hppb backintime (root): WARNING: Inhibit Suspend failed.
Feb  4 22:19:02 hppb backintime (mauro): INFO: Inhibit Suspend started. Reason: take snapshot
Feb  4 22:19:02 hppb backintime (mauro): INFO: Inhibit Suspend started. Reason: take snapshot
Feb  4 22:19:02 hppb backintime (root): INFO: on process begins
Feb  4 22:19:02 hppb backintime (root): INFO: Profile_id: 1
Feb  4 22:19:02 hppb backintime (mauro): INFO: on process begins
Feb  4 22:19:02 hppb backintime (mauro): INFO: Profile_id: 1
Feb  4 22:19:02 hppb backintime (mauro): INFO: on process begins
Feb  4 22:19:02 hppb backintime (mauro): INFO: Profile_id: 2
Feb  4 22:19:03 hppb /qt4systrayicon.py: INFO: [qt4systrayicon] begin loop
Feb  4 22:19:03 hppb /qt4systrayicon.py: INFO: [qt4systrayicon] begin loop
Feb  4 22:19:32 hppb backintime (root): WARNING: Can't find snapshots folder !
Feb  4 22:19:33 hppb backintime (mauro): WARNING: Can't find snapshots folder !
Feb  4 22:19:33 hppb backintime (mauro): WARNING: Can't find snapshots folder !
Feb  4 22:19:34 hppb backintime (root): INFO: Unlock
Feb  4 22:19:35 hppb backintime (mauro): INFO: Unlock
Feb  4 22:19:35 hppb backintime (mauro): INFO: Unlock
Feb  4 22:19:35 hppb backintime (mauro): INFO: Release inhibit Suspend
Feb  4 22:19:35 hppb backintime (mauro): INFO: Release inhibit Suspend
Feb  4 22:19:35 hppb /qt4systrayicon.py: INFO: [qt4systrayicon] end loop
Feb  4 22:19:35 hppb /qt4systrayicon.py: INFO: [qt4systrayicon] end loop

From this log it seems like the "Can't find snapshot folder" was produced about 30 seconds after the device connection, but I can state for sure that message in the tray icon appeared immediately after I connected the device (and not 30 seconds later!).

Also, shouldn't the schedule start as soon as the device is mounted, rather than when the device is connected? If auto-mounting is not enabled (or does not work for some reason), the backup job won't be able to start in any case... what do you think?