Confirming this.... I have yet to find a way to keep TuneIn logged into my personal account.
I log in using the QR code and it's all good until I get out of the car.... It then defaults back to the Tesla account.
I have looked through the account online at home and it shows the Tesla as being an approved account, but when I get back into the car, 99% of the time it's logged back out to the Tesla account.
So, one must just assume that tis will get fixed in a later update...
Until then, I have been just searching out my podcasts and marking them favorite.