More than likely, the center spindles in the adapter are not turning. Check to see if they exist and if they do, that they are turning freely. If not, trying to free them up. If no center spindles, then check to make sure it's fully loading and not off center or otherwise not seated properly. I would also recommend that you find, borrow or buy a blank cassette tape and see what happens with that. Many cassette tape players will eject the tape when they reach the end of the tape and the spindles stop turning UNLESS they have an auto reverse system.
Yeah, I'm old school.......... what of it?!?!?!?!?