TOTO uses a "three points of contact" approach on the Drake, but I don't know about the II. Because you are looking for contact in 3 places, it's easy enough to see on the Drake when you have it sitting correctly and have tightened enough. And when it's done so, the tank is firmly in place. One possibility is that the installer may not have put the sponge gasket on the bottom of the tank down squarely over the flush hole when starting to tighten, so that your tank may be actually pulling in a little at an angle. I have seen that on a toilet I fixed, and when I removed that tank and when replacing it started with the tank perfectly vertical, and then tightened slowly and alternatingly, pulling the tank straight down, the fit was amazingly better. The previous guy had even shimmed it to reduce wobble. In fact, just me installing it CORRECTLY resulted in no wobble with no need for tricks or fixes.
Bottom line is that the tank shouldn't wobble, and Toto's china is consistent enough that it isn't a manufacturing tolerance defect. He just didn't do it right. You paid to have it put in by someone, and presumably you did that so it would be put in right. It wasn't, so call the company that sent him and have them send someone else to fix it right. You will be impressed when you see how well it works when it is done right.
That "takes time to seat right" also sounds wrong to me. While maybe true in some cosmic sense, the flush nut sponge gasket is "seated" when it is properly positioned and then compressed into place by tightening the bolts. Given that the tank isn't supposed to move, I don't know what he thinks is going to cause it to seat better in the future in the sense of reducing wobble.
Also, just because no water is coming out between the tank and the bowl doesn't mean that it has been tightened enough or angled correctly. That sponge gasket is firm but pliable, and it can block leakage today without being sufficiently-compressed for the long haul that's intended, or for the tank to be properly secured.
Maybe he could have gotten some guidance by actually reading the directions. Maybe you would do well to print the installation instructions out (they are available online) and read them, so you know what the process should have been. Although it ain't that hard, the result isn't what it should have been. so it's likely that some aspect of the process wasn't what it should have been.
EDIT: I went back and looked at the install instructions for the Drake II. It uses the same booklet as for the original Drake (i.e. one booklet for multiple model #s, including Drake II). So the three points of contact instruction goes for the Drake II as well, which makes it easier to see whether the tank is installed incorrectly.
As to Jim's question, Toto does indeed instruct that you put a washer and nut on the bottom outside of the tank opposite the rubber washer and bolt head on the inside, then mount the tank on the bowl and put another washer and nut on the bolt to attach the tank to the bowl.
FWIW, because I'm not persuaded that the tank is being pulled down level against the bowl, I wouldn't try just tightening it more; if it is already pressing against one or more of the points of contact but not the others, you could crack it. I would try to make sure that it starts off level, and is drawn down towards the bowl level through even tightening of the nuts. Again, I'm not a pro, but that's how I have gotten every one of my tanks, on new toilets and rehabbed ones, nice and level and wobble-free.