I change my mind. I don't work at Mesa so I don't know what you mean by duty off. If airport reserve was added to your schedule anytime prior to setting the parking brake of your last flight, no matter if it begins 1 minute or 1 hour after your last flight, it is legal provided it doesn't violate your FDP you calculated.

Ex: Your RAP starts at 4am. You are called at 8 am. 14+4 gives you 18 but the rule states you are limited to 16. You must be done at 8pm. So, let's say you are only scheduled for 2 legs and are finished at noon. As long as it was added prior to setting the brake, you can be scheduled for any flight or reserve as long as it ends at 8pm when you must enter rest. So, you could have 3 hours "off" but your clock doesn't reset. You must be put to rest at 8. If the company wants to give you 30 mins off, that's their problem. They don't have to notify you prior to the brake being set but it has to be added to the schedule for it to be legal. If it is not added and you call and there is nothing or you check and there is nothing, any further additions would be illegal as you were put to rest when the plane was parked.