I don't have great panniers myself -just cheap ones that seem to do the job ("Giant" brand ones I bought many many years ago). I keep intending to get some new ones that are better -primarily because I don't like the attachments -simple open ended hooks that go on the top rack rail, and a bungee cord like elastic with a small hook that fastens to the bottom of the drop out.
I've never been entirely comfortable with the attachments -I always thought the possibility of the pannier jumping off the rack was just too much, particularly since the elastic cord with the small hook to the drop out isn't very strong. I did have some Performance panniers that I used to tour Europe that had a locking mechanism on the top rack rails -but (in retrospect somewhat regrettably) sent them back when the stitching started to come apart on one of the panniers. Of course, now I wish I'd just spent the time to re-stitch them up. But I digress:
The way I make my current panniers more stable is to take the two handles (assuming you have carry handles) and wrapping each one around the top rail until they are tight -this really ties the panniers down to the rack. I then use a very small bungee cord to maintain the tight tension and keep them from unwrapping from around the rail. I reckon it would take the rack coming off before the panniers do. I've used a small bungee cord, but next time I tour, I think I'll use a small compression strap for the extra stay in place security and the fact that a small bungee cord could conceivably break -though this means a little more messing around when I need to remove the panniers.