Practice decision
This to me is a practice decision and perhaps even as specific by particular insurance or patient.
For example, if a patient has Medicare primary and Cigna with $20 copay 2ndary, the patient will owe UP to the Cigna $20 copay. But if you wind up with 99212, the patient will not owe the full $20.
In our practice, any patient with Medicare primary, we tell them we will bill both insurances and will get a bill for any responsibility. If a patient has 2 commercial policies, we generally ask for the primary copay and if the patient has any objection or states the 2ndary will cover the primary copay, we don't collect and tell them we will bill both and will get a bill if any responsibility.
To me, it basically depends on whether you would rather deal with the hassle of potential refunds or bill the patient later.
And that's my 2 cents. Hope it helps.