Most swivel knives come with an open saddle design on top of the pivot. The general idea is fairly simple to understand – you need to rest your forefinger there and put pressure on the knife when needed. Since it is open, large and thick fingers will also fit in.
Then, you will find swivel knives with a closed saddle design – or almost closed. Usually, those saddles are quite large, so they can accommodate most people's fingers, but there are a few exceptions too. They provide a bit more control, as you can also slightly lift the blade when carving.