[oldman]

Take the dome off if you're available to mist them every six hours or so. Seeds have aa preferred temp rage for germination that tops out about 85F for most tomatoes.

If you use a heat mat the heating mat heats the soil, but the dome holds heat as well as moisture in. The biggest issue is that the moist air hold more heat on the plant than warm soil does. Too wet and your plants are in a sauna, too dry and the water ends up on the inside of your dome and not in the soil.

I use a dome with peppers but only until half have germinate. I still have better luck on later season flats where I skip it. Tomatoes I sometimes use a dome, but never with a heat mat. I look at flats a couple times a day and use a spray bottle to keep everything moist, but not wet. And every couple days I move flats around so I can judge weight to see if they need a better watering.

Once you have germination I'd recommend moving the whole flat under lights. Once gernimation has started I usually put the heat mat on the same timer the lights are on. You don't want to divide up the insert and the light may give seeds that are planted deeper a push to get to the surface. You can have too much heat from a heat mat, but it's not likely you're going to get too much light from home plant lights. You may need to lower the light closer to the seedlings to get enough. And if all the heat i coming from your lights they may be too close, you might need better air circulation, and the dome probably exacerbate s the heat issue.