Your thinset should be like peanut butter. If it is too thin then you could have possible issues with mosaics and flooring. Basically you could push down to bare floor or close to it.
A 4mm trowel is perfect size for most mosaics. I think that your issue is that either you aren't combing the area well enough after dropping down your thinset or possibly you are pushing down to hard.
The installation method for any tile but especially a mosaic is to comb the area in a direction, sit the tile on the area, then gently press the tile into the thinset perpendicular to the thinset streaks back and forth. If you were to just press straight down hard you would have a lot of thinset in between your tiles and as mentioned before not enough behind the tiles.
Also you will always have a little spillover. You don't have to clean out all of the thinset in between the tiles. Your grout will bind to the thinset fine so you just need enough room for the thinset to not show.