Comment 3 for bug 286577

In Kubuntu I have enabled "restore previous session on login".

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If that is the case, I am going to guess that this is because Thunderbird registers something with KDE and AllTray does not.
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I think that this is the problem.
I presume that "restore previous session" is done by saving the running applications into a list and launching them back when log-in is performed.

AllTray should check if "restore previous session" flag is set and if it is, should change the start-up command of each owned application which is running when log-off is performed (owned application = application started through alltray) .

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I don't understand how 5.3 and 5.4
lead to 5.5 (Thunderbird not running).
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Is not 5.3 an 5.4 is 5.4 = 3.0. Close the thunderbird from "close" button and see that thunderbird process is not running, which means that tunderbird was not started through alltray.