FaceTime conflict on home network

My wife and I have different Apple IDs and both share a MacBook Air and an iMac with our own separate user settings. I find that when she uses FaceTime on the iMac and I try to use it at the same time on the Air, I have problems connecting to the other caller. For example the caller tries to connect to me and gets the message that I am not online. At the same moment I see their contact come up in the sidebar. The workaround is that I then call them back, but it’s frustrating and I’m not sure why it’s happening. In addition, calls made by me seem to crop up on my wife’s FaceTime history as if they had been made by her which they have not been. It’s as if the boundary between the two accounts is porous. This is all taking place on the same network. Thanks for your help!