My tic tac wheel is second second hand - but I noticed mine a little unstable and asked someone about, you have to have it on a complete flat surface, cant have anything under the legs at all otherwise it wont be stable and will do similar to what you said.
As for the swinging its to do with the hedgehog, they can take any size hog, but sometimes it takes them a while to balance themself on the wheel, once they can do that it should swing less!
The swinging may be worse if the wheel is unbalanced
The only reason I can think it might seem like its tightening up is that something may be wrong, it doesn't do that on mine (and mines all rusted but I did get it for free)
I think contact them and explain it and see what they say if you haven't had it long they may get you to send it back for them to look at/replace. They are nice people.