After hours code "times" vary by insurance. Typically they start when the insurance company closes for the day. Like for example Anthem, 5p. When you go through credentialing you specify your office hours. If you see patients outside of these hours, it's after hours.
If a patient has an appointment scheduled at 430p and they aren't seen until 615p... I would definitely not charge the after hours fee. The reason why is because most insurance contracts state an amount of "waiting time" that is acceptable to their standards. A 2 hour wait, even though we all know it happens, is not at their standards. So, if you charge the after hour fee, the patient gets an EOB or bill, and calls insurance and argues that they were there at 430p.. you might get dinged.
I count it when the patient steps foot into the door.
Food for thought -- I know of a clinic who decided they were going to establish a new tax id for after hours care because it became too overwhelming with the insurance billing. So, they accept no insurance, and charge a flat rate of $50 per visit. Only acute care, no preventative encounters, no refills.