Trouble playing different content simultaneously in different rooms

Can someone please explain how room control is supposed to work? What I’m experiencing appears problematic.

The setup:

Two rooms: A and B. If it matters -- room A contains a One SL; room B contains two Fives in a stereo pair.

Two people: Person A in room A, person B in room B. Each person is using the latest Sonos app on an iPhone.

The problem:

Person A is streaming a radio station in Room A, from that station’s web site, using AirPlay on the person’s iPhone.

Person B wants to stream a SiriusXM station in Room B. SiriusXM is accessible via the Sonos app on person B’s iPhone.

Person B clicks the Rooms icon on his Sonos app and sees both rooms. Room A is checked and indicates streaming. Room B is unchecked; no streaming shown. What does he need to do start streaming something in Room B without affecting what’s happening in Room A? If he checks Room B (so that both rooms are checked), his streaming choice starts playing in both rooms. If he unchecks room A and checks Room B, his streaming choice starts playing only in Room B, but he’s now shut off what’s been streaming in Room A.

The solution: ???  Am I missing something very basic? (If so, apologies in advance.) Any help would be greatly appreciated.