I can also confirm this issue: I have 2 premium accounts. When selecting the not-standard-selected account from the dropdown at the topleft, the previously selected account is still used when pressing play.
I have logged out and back in, and added both accounts to the launcher again, and the problem persists.
The issue appeared about 2 days ago for me when the launcher auto-updated itself.
Reinstalling the launcher with the latest version from Mojang does not fix the issue
I found out I had beta launcher enabled.
The issue seems to be in the newest beta version
disable beta launcher in settings and after restarting the launcher the issue will go away