In my opinion the previous thinset would not necessarily have to be removed. Nor would it have to be filled, IF
, the tileguy knows what he is doing. With tiles that size however the floor must be plane. The bigger the tiles the flatter the overall floor must be. This doesn't necessarily mean smooth. Smooth and flat (plane) can be two different things.
Once an installer has determined a suitable layout, usually based on "balance" he can begin installing tiles anywhere, IF
, the tileguy knows what he is doing. He doesn't have to start in the center of a room, I never do.
I can assure you that polished porcelain will tell the story quickly if the tiles are not installed on-plane. I would suggest the use of a levelling system, either Tuscan or Raimondi but this won't likely come from the cheapest installer you can find.
Arizona is like a few other states where things are done a little differently and at a very low cost. You can't hire cheap and expect perfection.
Arizona is also a place where tile is laid up-to the baseboard as a routine practice. I personally would discourage that technique. But, here-again, it is do-able IF
the tileguy knows what he is doing.
My thoughts are you would have been better off hiring a reputable store to provide an installer in this case. The odds of having some recourse with a store are much better than using an independent installer. That may sound weird coming from me because I am an independent installer but in this case you have no protection if the guy does a lousy job then scats.
All I can suggest is to withhold payment until he is finished and you are happy with his work.