Purple underside
 

Do these look okay? 2 weeks old

They look OK for their age. The purple should fade away slowly as they grow bigger.
On larger tomato plants if there are still purple undersides, that means there is a problem with phosphorous uptake. That can be caused by insufficient fertilization of course but it can be caused also by cold soil or overwatering.

Mine are the same way. They always do great once they are planted

I always get purple leaves or stems. Once I plant them, they do just fine...

UPDATE
 

Taking them out from under the growlights into the sun they have been doing just perfect. Thank you.

Timely -- I was just about to ask about this, also. For me, it seems to vary quite a bit by variety. For instance, Early Wonder has quite a bit of this, and Patio none (planted in the same container on the same day, etc.), Hybrids (in general) have much less for me than the OP's. My experience has been that fertilization doesn't seem to help, but as others report, once outside and out of the grow lights, it goes away quickly. Interesting -- wish I knew exactly what was going on.
-GG

Just anthocyanin pigment accumulation in the leaves - probably a result of high light and/or the spectral spread of artificial bulbs. Some of the "blue" tomatoes color very strongly as seedlings.

I just read, can't recall, that the purple in seedlings when starting indoors is usually the lack in an ultraviolet spectrum that grow bulbs can't deliver that the sun can, so the seedling makes up for it, this we see purple

As PhilaGardener said, many of the blue varieties are more prone to purplish blue tones. Coloring of leaves is often associated with genetics and not necessarily a deficiency. Before running to a "trusty" bottle of fertilizer, get to the know the variety you're working with. The ruination for many new gardeners is over-feeding and over-watering.

What variety are you growing? What are the room conditions - temp, humidity, light source etc.. What are you feeding with, if anything? Still early to be giving them much more than a 1/4 strength grow fert. A good indication that they're hungry is when the cotyledon's (first set of leaves) begin to yellow. I will say that your soil mix looks awfully fine and wet, possibly lacking aeration (not sure of the mix beneath the top), is there any perlite in the mix? With all that being said, they look fine for their age, just give them some time and let the soil dry out some before drenching them again.

My three week old seedlings have purple under the leaves also. It's a really strikingly deep purple. Is this also from lack of light? They're in cruddy nutrient deficient soil from outside. (I knew it was a bad idea but I had to try it once.) Adding dilute liquid fertilizer and a pinch of rock phosphate didn't help. I got real seed starting mix later and planted more. Though, they don't have true leaves yet so I can't tell if better mix made a difference.

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Can you repot them into your better mix?
The purple (temperature related) doesn't bother me at all.
Don't like to see that leaf curling though.

Yes, I agree the "cruddy nutrient deficient soil from outside" is the problem with the curling.

Should I re-pot in seed starting mix or regular potting soil?

Also, why would garden soil cause leaf curling problems? Is it because the texture and water holding properties make it bad for containers or is it because of the nutrient deficiency? I hope it's not something else that will cause problems when I amend the soil and transplant outside.

Repotting them in either will be an improvement along with some light liquid nutrients.
Your garden soil looks to be mostly clay with little organic matter so poor structure and poor biological activity for nutrient cycling. If the soil holds too much water and doesn't drain properly the roots will also suffer from a lack of oxygen. All that adds up to nutrient deficiencies. The thin appearance of the leaves, the striking purple color and the curling down along the leaf margins ifs evidence of that to me. Even fertilizing in those conditions can't help if the roots are unable to uptake the nutrients
Repot them up and see what happens with new growth. If a plant is in an unhappy situation for too long then that may lead to permanent stunting.

Those seedlings look to be suffering from a phosphorous deficiency, you need to feed them.
I start a couple thousand tomato plants, and I have had the same issue, no big deal if you just feed them.
As Ray pointed out it can also be cold soil or a combination of both.