Another near myth in the hobby is that beneficial biology only lives in filters. In some regards, manufacturers would like that to be true for increased sales of filter bio-medias. It just isn't true....
As for filter swapping, there really is no single time rule. For instance, in an established aquarium (6 months or more), there is more beneficial biology in the tank, especially the substrate, than in any filter (consider the surface area). In addition, if you have plants, especially fast growing floating plants, they will consume ammonia as their nitrogen source eliminating much of the ammonia->nitrites->nitrates.
So in some, if not many/most, systems, you could swap filters right away and never see an ammonia spike.
In a new setup, you might want to wait a couple of weeks just to be conservative, but in any case of filter swapping, you just need to monitor the fish for any signs of stress (like surface air gulping), flashing, and the like, and take appropriate measures. (I always have Safe or Prime on hand in the event there ever is an unexpected ammonia spike).
