@Shachar
Based on my experience, if you soak the paper, then you want your sponge to be damp but not saturated, which is how I've used these in the past. It does seem that you can just add the dry paper to the saturated sponge and it works out reasonably well.
I've also run into issues with the paints getting very thin and runny. The brushes sometimes get quite wet and I think I'm giving them light squeezes when I don't mean to, ending up with a much wetter mix than I wanted. I've been running the brush over the back of my hand to double check that it isn't too wet before I start with a new color and that seems to help.
The wet palate + water brush combo is certainly a new challenge for water management!