Toilet not stable - what to do?

My mom had her bathroom fully remodeled. There are new tile floors and a new toilet too (AmStd Cadet 3). At first the installation seemed solid, but after 1 month the toilet started to rock back & forth a little. She called the guy who did the work and he tightened the bolts a little more. However, my mom noticed that the tile floor is somewhat uneven. The guy refuses to re-do the floor and said he will come back with clear silicone caulk and will caulk around the base of the toilet and that should do it. I know that caulk is used as a sealant and sometimes as glue, not as support for rocking toilet. However, I realize that if the gap is very small and he puts some caulk in the gap, once it hardens it will provide some (minor) support. She's concerned about the procedure.

Questions:
1) Will caulk somehow spoil the toilet base or tile?
2) Can this steady the toilet?
3) Are there any other concerns about the procedure?

Thanks in advance.

Are you sure it's the floor, and not the bowl of the toilet.

American Standard bowls tend to need more shimming then other brands.

It should be shimmed first, and then caulked.
All bowls should be caulked when installed.
But since the floor guy did the toilet install, rest assured that a plumber would have done it right.
They would have shimmed that wobbly bowl, and then caulked it.

Terry, thanks for answering.

I assume that the bowl should be shimmed prior to tightening the nuts, right? First, make sure the bowl is stable by shimming it, then tighten the nuts, then caulk?

Yes

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You need to shim the toilet before you tighten the bolts or you risk cracking the toilet. Then, the bolts don't get tightened much. Porcelain doesn't flex, it breaks. So barely tight is all it takes. The caulk also helps keeping it from moving around and keeps crud from wicking underneath, say from mopping the floor, little boys missing the toilet, etc.