was wondering if I have to load them more to the max of what my manual says is safe to get the action to cycle or will it cycle well on the min. loads?
NO, chamber pressure has nothing to do with cycling the action of a semi-auto. What cycles the action is port pressure. Port pressure is cause by the amount of gas or gasses that travels down the bore and enters the gas port. Hence port pressure. Slower burning powders produce more gasses thus more port pressure.
A fast pistol powder loaded in your mini can produce chamber pressures well above Max and still not cycle the action, why? Cuz fast powder burn to fast to produce sufficient port pressure to cycle the action even though the chamber pressure can be excessive.
Load your Mini according to published data and stick with med to slow burn powders and you will be able to load them from weak to heavy and still cycle the action. I would not go faster than 4198 for the Mini-14.