Okay, you're confusing a few things.
You are correct to stop tightening the tank-to-bowl bolts as soon as there is any china-to-china contact and if you have kept the tank vertical while tightening slowly, a few twists on one side then a few twists on the other side, all china contacts should occur basically-simultaneously.
Compressing that rubber gasket isn't going to prevent leaks while the toilet isn't flushing, because no water should be coming through there when it isn't.
The likely issue is the tightness of the flush valve mounting nut. Usually, it's best to snug that thing up to hand-tight plus 1/4-to-1/2 turn before slipping the sponge gasket over it.
However, the dumb system American Standard uses for the Cadet 3 tank-to-bowl washers and nuts is leak-prone, based on many reports on here. If the tank isn't cracked from the factory, and your flush valve mounting nut is snug, then there are two possibiltiies. First, you may have a leak between the flush valve gasket on the inside of the tank and bottom of the tank, which one might remedy by sanding around the hole that the flush valve sits in (i.e. pull the flush valve, use fine sandpaper to smooth out any rough spots, and reinstall the flush valve). That is less-likely than a leak from the tank to bowl set or the mounting nut just being too loose, however.
Second, you may have a leak around the tank-to-bowl set. Many pros on this forum just discard the AS tank-to-bowl hardware and replace it with a standard tank-to-bowl set, double-nutting the installation. IF that is the problem, you sand around the bolt holes and use a good brass set like this Sioux Chief one, and you're likely to get no leaks. (Any decent brand of bowl set will do: what you are looking for is solid brass or stainless steel, with a big bolt head and two sets of rubber washers, metal washers, and nuts. You absolutely will not find this at HD or Lowe's.) If you go that route, the proper installation method is: bolt head and one rubber washer inside the tank, metal washer and nut on the outside of the tank, THEN mount on the base, then use rubber washer, metal washer and nut, in that order, under the base to secure the bolt (and thus the tank) to the base. Never put the metal washer inside the tank; it causes leaks, although a zillion brain-dead handymen insist that's the right way to do it; it isn't, it's exactly the wrong way to do it. The bolt head is designed to be the thing that seals against the rubber washer inside the tank; a metal washer just keeps it from compressing properly into the rubber (and besides the metal washer is needed to secure the first nut on the outside of the tank).
Bottom line: first thing I would do is pull the tank, remove the sponge gasket, and snug up that mounting nut for the flush valve.
Come back with any questions and/or to report how it works out.