You shouldn’t set up a new Apple ID on a device, when that had recently been done already on that device with a different ID.
There is a mandatory wait time of 90 days between such registrations as “associated device”.
This is about using Apple Music on a device that had already been registered for a similar service with a different Apple ID just yesterday.
This is unrelated to the subscription type (Individual/Student/Family).
This doesn’t affect using the subscription on other devices, that had such “associated device” registrations longer than 90 days ago, or never before (new).
About your associated devices - Apple Support
“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.”