Hi!
Thank you for the proper details, it helped a lot.
The problem was, that when the plugin tried to check if the tables were created, the wordpress core returned the lowercase name of the database tables, while the original names were in lower and upper case as well. This caused a mismatch and it falsely returned.
I have made a correction in the code via FTP to ignore the case, now it works as expected. I will make sure to include this fix in the upcming release, so you don’t have to worry about it anymore.