New American Standard Cadet on a new ceramic floor

I've just set a toilet an abs flange on a new, ceramic on concrete, floor. I've tighened the closet bolts snug, athough I've choked up, all the way ,on the wrench to limit the torque I can apply. The floor tile is level but if I try hard I can get a slight rocking front to back. I have sat on the thing and tried rocking it side to side and it is stable, but if I lean back against the tank it will rock slightly. about a 1/16" or so movement.
I know Lonnie may say "well don't lean back then" but seriously, I'm really scared to snug these bolts up any tighter being it's on ceramic tile. I have no experience setting toilets on this type of floor.
The flange is down flat on the tile. it is however not screwed into the underlying concrete. Hey, I may be answering my own question here but I believe this is the problem. Being the toilet is longer front to back it can easly lever when a force is applied. Now that the flange is glued in, oops what can I do to anchor it into the floor? Any ideas?
I thought might drill thru the tile into the conrete, but in order to use a standard anchor bolt I'd need to drill out the flange while trying to make a large enough hole. Other than using expanding mortar to hloe screws in I'm at a lose. please help. Or do I tihgten a little more?

I like to check to see if the flange is secure, if not then the concrete and tile will need to be drilled to hold the closet bolts tight. You can use "drop-in anchors".

If you set the toilet without wax first, you can check to see if the bowl rocks.
If it does rock, then shimming at the back is best, pinning down the front of the bowl.

Some wax rings with horns will hold the toilet up, causing a rock. This is why you check to see how things feel without wax first.

Thanks for the help. I did try it without the wax first and all was ok. That's what had me fooled. Anyway, yesterday, I bought a tile bit, a masonary bit, and the appropriate fasteners. Before going ahead, and out of curiosity, I checked for the rocking . Low and behold the darn thing was solid. I was really puzzled then. It was evident that something had moved, but what?

Anyway, I now believe that your explaination , "the ring was holding the toilet up", was exactly right. The wax ring I used was an Oatley with a rubber grommet attached. Is this the horned type you refer to?

Further, I removed the toilet and drilled the floor and secured the flange as I should have done in the first place. All's well now.


Thanks for the help.