I would say that you are not leaving the growlight on long enough or you do not have the plant close enough to the growlight. If it is the florescent or purple kind it needs to be within a few inches of the plant.
Also starting soil doesn't have any fertilizer in it so you will need to add it once the plants develop true leaves. You need to use one with a high 2nd and 3rd number rather than one with a high first number.
Tomatoes are heavy feeders and need to be transplanted into a soil mixture that is 50% compost and 50% garden soil. This and the fertilizer should help your tomatoes become happy and healthy. If it is working the leaves will curl up somewhat in response to the new conditions. This is normal.
Good luck with your seedlings