I expected to see transmission-daemon.service in /lib/systemd/system/, but it doesn't exist and there is nothing related to transmission there.
Other distributions (I think also including Debian) have shipped with the service.
ProblemType: Bug
DistroRelease: Ubuntu 16.04
Package: transmission-cli 2.84-2
ProcVersionSignature: Ubuntu 4.3.0-2.11-generic 4.3.0
Uname: Linux 4.3.0-2-generic x86_64
NonfreeKernelModules: nvidia
ApportVersion: 2.19.3-0ubuntu2
Architecture: amd64
CurrentDesktop: MATE
Date: Tue Dec 22 16:18:03 2015
InstallationDate: Installed on 2015-12-12 (9 days ago)
InstallationMedia: Ubuntu-MATE 16.04 LTS "Xenial Xerus" - Alpha amd64 (20151212)
SourcePackage: transmission
UpgradeStatus: No upgrade log present (probably fresh install)
Status changed to 'Confirmed' because the bug affects multiple users.