Tell the handyman, that a properly installed toilet bowl should not rock.
It needs to be reset with new wax, and this time he should shim the bowl before he tightens down the nuts.
I use plastic door shims. They are the best!
And then he should use polySeamSeal or something similar around the bowl.
In Seattle, we leave the back open. We don't have ants here, it's not Arizona.
We leave the back open in case the wax seal leaks. We have wood floors here.
In Arizona they caulk it 360.