I always use UDPP and usually use a base as well.
Most of the time I use pigments I have pressed, but some don't press well and some I haven't had time to press so I use those out of the lid. I always spray my brush with homemade fix, or in a pinch I will run the brush quickly under the tap and shake off excess water, before dipping into the pan or lid.
You will still get some fallout with certain pigments, especially the very frosty ones it seems. Use a kabuki to lightly dust fallout away, very light touch so you don't smear it on worse.