I understand you are using the Joomla! Popular Tags Module to show Tags. Please confirm that field Parent Tag, as in pic "popular tags00.png" below, is empty. This is because jD does not support 'nested tags'.
The Popular tags module lists the tags as illustated in pic "popular tags01.png" as below so that if you click on one of the Tags then it lists the content items with that Tag.
So the challenge is that if you add an existing Tag to a new Download created with jd3.2.59 then that new Download is not listed when ypu click on the relevant Tag.
Anther point I would like to know is was the new Download created in the Back End or the Front End?
Also are there multiple tags associated with the Download?
Please note I have tested the various combinations, and used the Module Popular Tags, but still cannot reproduce the problem.