I have an RCBS Partner press. I think it is the smallest they make.
I had a lot of flying primers until I started using a Lee Universal De-capper. I don't know why this is. I bought the de-capper because I wash the brass instead of tumbling it. So, I like to de-prim separately, prior to washing. The brass drains much better with a hole at both ends. And, the pockets get clean, along with both "sides" of the brass.
Before I got the Lee, I used to put a plastic tarp down before de-priming.
Dean Grennell mentioned this problem in one of his books. Seems he liked to work bare footed. I think he lived in California! He solved the problem by using an RCBS Model A-2 press that he acquired in 1959.
He said it deposits all the spent primers in a tomato can and he can work with his feet unshod without fear!
Best,
Rick