Twice a month my iPad Air 2 tells me someone signed into my iMac

[mattg3]

Seems like twice a month someone signs into my iMac and uses messaging at least thats what my iPad Air 2 tells me but it doesn't say where this is happening.I immediately change my Apple ID and even changed what I call my iMac and it still happens. I have two step verification setup and when it happens my iMac is asleep and when I it check out there is no sign the iMac is being used. I must admit I was still running Mojave on iMac but I just updated everything to Big Sur. Im hoping this will solve the issue. Is it possible the iPad Air 2 (with all security updates and IOS in place). being pretty old is just experiencing a glitch when it tells me my iMac and Apple ID are being used? Thanks