Most seeds like to germinate between 60 degrees and about 75 degrees. That covered cake holder could get well over 100 degrees out in the direct sun. Place the container in a location that is about 70 degrees and the moist environment in the enclosed seed starter should be about perfect. As soon as the seedlings are up, remove the cover and place the plants outside were they get full sun, if you are planting sun loving plants like tomatoes and bell peppers.
You didn't say, but I assume that you put drainage holes in the plastic cups.
Eclectic gardening style, drawing from 45 years of interest and experience. Mostly plant in raised beds and containers primarily using intensive gardening techniques.