When is the detection made as I suspect from what you said "I entered an Exclusion in the Expert Settings for the 'File Shield' but Avast keeps picking up the file as a false positive and it puts it in the Virus Chest." I suspect that it may being picked up on an on-demand scan as presumably this file only needs to have been launched once (not every time) ?
If that is the case then you need to enter the full path c:\program files\TransMagic\tmlicenselauncher.exe into the avastUI, Settings, Exclusions.
Have you submitted the file as an FP from the avast chest (if not I would try that, or send it again) ?