I like to start my seeds outdoors when there is no chance of frost, sometimes in larger pots (so I don't have to transplant tiny seedlings), trays, whatever is most convenient and on hand, sometimes sow directly in the ground, keep them in a shady spot sometimes, sometimes not. Then I don't have to worry about hardening them off or their getting used to outside.

Being in the south, maybe it is too hot although tomatoes love hot weather so long as they get enough water.

I'm way north of you, so the only time I start seeds inside is during winter or early spring a month or two before the last frost until it is safe to transplant them outside. But it is more difficult, I sometimes have to deal with damping off, leggy seedlings, and definitely hardening off outside which takes some thinking and being home.

And I'm no expert by any means, but I have experimented enough to know what usually works for me.