Seedlings, especially those newly germinated, are very susceptible to a disease called damping off. While damping off may be specifically caused by any number of microbes, it is always a result of overwatering. However, tender seedlings need a steady source of moisture, which makes keeping the seed trays evenly moist very important. That is best accomplished by watering from the bottom up.

Take some thin, polyester batting, about 1/4” thick, and line the bottom of the tray with it. Moisten the batting thoroughly, then place the newly planted seed cells on the batting. The water will wick up through the potting soil and reach the root. The plant will only take up as much water as it needs. 

When the soil feels dry to the touch, water the tray, not the plants. That should serve you well until you need to transplant to larger pots.

Spraying the plants to keep them moist creates a perfect atmosphere for water-borne diseases to thrive. Avoid it if at all possible.