No, they are not supposed to look like that. I never grew tomatoes under lights, but those are far too long and thin. As soon as they develop any more leaves, they will collapse because the stalk can't carry the weight of the leaves.
Ideally tomato seedlings should look more like this or this.
To answer a follow-up question from the OP, yes, start again. You can't make those seedlings get back to the shape they should be!
You can re-use the potting compost. Just pull out the seedlings and plant new seeds.
