It's not important that the tank touch or that it may move some.
Some tanks move and some don't.
When we install them, it looks like this.
I find that the tanks pull down pretty well.
However, if you feel the "need" for a solid situation, there are molded on tanks. There are many one-piece toilets to choose from.
Most come with a nice seat, are slightly quieter, and are easier to clean.