Fitness+ working out concurrently, different workouts

Hi, my partner and I both have apple watches series 8 and 9, separate apple IDs, Apple TV and subscription to Apple One Premium already setup in family. We tried to workout at the same time in separate rooms (same wifi) doing two different workouts within the same workouts area “strength”: I was using Apple TV connected to my account, he was using his iPhone connected to his account. He couldn’t use it because the app was warning that a workout was already ongoing but when trying to start meditation workout it worked. We couldn’t figure out how to solve it..shouldn’t we be able to use fitness+ independently with a family setup? Is it not possible to workout on different videos but in same workout type at the same time?

Thanks a lot for the help!