I've never had a problem as long as I let the tent air out and dry at the first opportunity. That includes one trip where there was solid rain for a week. The tent was (and still is) fine after I made sure to let it dry thoroughly once I got home.

OTOH, our experience was not so good with a tent we borrowed from my inlaws many years ago. They told us to look for the tent in the rafters of the garage and we found that my wife's sibling had returned from an outing a few months earlier with the tent soaked from a thunderstorm and stored in a plastic bag since then. A hot garage and trapped moisture inside the plastic bag proved to be excellent conditions for growing mildew and the tent never recovered.