Help! Toto ultramx rocking side to side- does it need to be shimmed?

My handyman is installing my toto ultramax and it is rocking side to side. The gap between the floor and the toilet is 1/4". Do we need to shim it? It sits on tumbled travertine 8" sq and floor tiles are not level. Wax ring is sealing fine. What material to use for shims...someone mentioned pennies on another thread.
Helphelphelp

I have used composite shims available at the big box stores.

A toilet may not leak and still have a compromised wax seal. If your toilet is rocking, it MUST be pulled up and reset with a new wax ring. Each time it rocks one way, it compresses the wax. WHen it rocks back the other, the wax does NOT rebound like a spring, it tears an opening. Yes you MUST install some shims to keep the toilet stable, but it can't be done now without redoing the wax. You can, however, figure out now where they need to be. Normally, you'd set it in place without the wax to determine where the shims need to be, pull it off, place the wax, then set it back down onto the shims so it gets that one chance to smush the wax and settle into its final position.

If it is rocking because the floor is unlevel, then it needs shimming BEFORE you set the toilet, but if it is rocking because the flange is too high, which would lift the toilet 1/4" above the floor, then no amount of shimming will prevent it from eventually leaking.