Most fins develop a warp or "set" over time, as the trailing edge gets stretched by resting against uneven surfaces. This acts like a trim tab on a wing and tries to pull the fins over to one side or the other. If your Drive is reasonably well lubed and adjusted (without a lot of friction) the Drive is often able to advance one pedal forward (with your feet off the pedals) as you move along -- the faster the speed, the greater the tendency. About the only Drives that don't so this to some extent at about 5+ MPH are the ones that can't overcome the excessive friction (i.e. in need of a tune-up), and those with new fins.
As to vibration or chatter at speed, this is not normal. I would look carefully look for a loose mast, cut fin, cracked outhaul, loose cable, etc. If your fins are looking a little beat up and everything else appears good, replacing your fins may solve the problem.
Let us know what you find!
BTW, a cardboard sleeve is a great way to protect and store fins: I dry and sleeve them as soon as possible when coming off the water -- they stay in much better shape and perform better!