So far as I recall the Paterson Super System 4 tanks and reels don't/didn't have these clips. This is because the S-S-4 reels have a few mouldings inside, against the tank-core, to give more of a springy grip on the core.
I have seen a much older Paterson tank (really old, before the 'System' designs) with slightly different reels, though nominally the same size, and a clip. Probably there are 'old' reels being used in 'new' tanks, and vice-versa, which gives different results depending on wear and tear of the gear. An elastic band wrapped round the core, above the top-most reel will stop unwanted movement, as mentioned by several other people.
I just checked three different makes of 'Paterson size' reels and these days they all seem to have some extra moulding on the inside. On my Jobo reels there is no friction-increasing feature, but I haven't noticed reels moving in those tanks when used for inversion. It obviously wouldn't be a problem in Jobo rotary processing either.