What exactly do you mean by, "badly fitting"? A cover that is a bit too large, typically isn't a problem. A cover that's too small, is.
As far as, "vapours/hot air escaping from under the tub cover during filtration", this can be normal if ANYTHING, such as air from an open air dial, or ozone being injected into the spa, is happening (anything that goes in, must come out...or the entire spa will blow up like a balloon, and POP).