Misting is not a good watering technique. This just wets the top layer (where there are no roots). Hopefully you have cut drainage holes in your cup. (I normally just do 4, but some growers will punch a bunch of holes, and you pretty much can’t have too many).
Use a small glass and pour a small amount around the edge of your cup (trying to keep the stem area dry). Wait a minute or so and do it again, wait, again until you start seeing run off. (If your soil gets dry the water may pond on top. If so wait until your first pour totally soaks on.)
In the cups you don’t have to worry about having excess runoff (like you will after up potting, because your shouldn’t be feeding at this point and aren’t going to have a build up of salts.) Stop watering after you start seeing the run off. If you take it slow your pot should be fairly wet at this point, but not completely soaked. Use the (previously mentioned) weight technique if you’re unsure (but will soon get a good feel of the weight just by hoisting the cup).