(Another) Paper Towel Method question

[ARgardener]

First off, I'm using coffee filters and not paper towels.

I'm wondering- after I transplant the tiny seedlings to soil, should I cover the soil with some plastic until the seedling emerges to keep it moist? Or should I simply sow and leave uncovered?

Also, what's the time frame for this method?
I'm starting tomato, peppers, and eggplants. So far, on day 3, I've got 3 sprouts from one variety of tomato. My other 4 varieties of tomato, my 2 of eggplant, and my 6 of pepper show nothing yet.
Just wondering so I can know when to start freaking out