The whole thing is described at View and remove your associated devices in iTunes.
It seems Apple allows to connect several devices, without any problem, but at the same time it has some restrictions and limitations.
You can have ten devices (no more than five of them computers) associated with your Apple ID and iTunes at one time.
You are getting this message because of their AppleID policy:
When you try to associate another Apple ID with a device that was already associated, you might see a message that says, "This device is associated with another Apple ID. You cannot associate this device with another Apple ID for [number] days." Depending on when you associated your device with your Apple ID, you might need to wait up to 90 days to associate the device with another Apple ID.
The iTunes account scenario and a 90 day wait between transfers is a seriously ridiculous constraint. But it feels there's no other way-around as per discussion here: Multiple Apple IDs on one Mac