I think the correct way of doing the upgrade to version 2020 should've been to first uninstall the 2015 version , then run the Acrobat Cleaner and Repair tool, and last perform the installation of 2020.
If this wasn't done that could be the reason why you're macOS still loads up 2015 even though you did installed the 2020 version. Seems like old traces of the old installation were not removed completely (I may be wrong though).
It is the same adobe id on both machines. The account is a work account, but the PC laptop is a personal computer. The imac is in the office and I am connecting to it remotely from home. I know I installed Acrobat from the CC app on my pc, but our IT guy installed 2020 CC on the work mac Aug 2019. The CC desktop app on the mac shows Acrobat as being up to date, but when I open it from there, it is the old version.