I think you are off to a good start. Your seeds have germinated and that can often be the biggest challenge. Great job so far! The yellowing you see could be caused by many things. 1. plants need more light, 2. over/under watering, 3. fertilizing too much/not enough or 4. pest problems.
Its really hard to tell what might be going on with your plants but here are a few things to consider:
Those light bulbs you showed are tinted blue in order to make house plants look more green. I'm not saying they can't be used to grow plants I'm just saying they are not made for specifically for growing plants. I'm not an expert on indoor plant lighting so I'll let someone else chime in advice on what type of bulbs to use.
What I can tell you is your tomatoes look pretty good so far and just a bit leggy. Notice how the ones in the back look taller than the ones closer to the light in the front row. That is a sign the ones in the back row are not getting enough light. Try putting the lights directly overhead a just few inches above the plants. You will have to move the lights higher up as the plants grow so they don't touch the light bulb. Additionally, I've heard that keeping lights on a plant 24 hrs a day can actually slow their growth. Like humans plants need a chance to rest at night. Try switching to 16hrs on and 8hrs off.
Its hard to tell but your soil looks a bit dry in the photos. It also looks like you have your tomatoes in a tray and that the seedlings are in a peat moss pots. If this is the case you can actually water by filling the tray with water and then letting the soil, peat moss pots and tomatoes absorb the water. This helps keep water off the plant's leaves and stem which can cause common tomato diseases.
How much water will be dependent on many things but I would start by putting ~1" of water in the tray. It should all be absorbed by the plants in an hour. If there is still standing water after 1hr pour out the extra and add water less the next time. A simple rule is to water whenever the soil feels dry if you insert a finger to the first knuckle. Note: This may be a more appropriate test when you are watering from above instead of from the bottom. Watering is tricky - too much and rot is possible too little and plants dry up. If what you are doing seems to be working then feel free to stick with it.
For best results fertilize plants every week or two. It is probably easiest to use a liquid fertilizer you add to the water such as fish emulsion, liquid kelp or Vermicompost tea. You can also add fertilizer to your soil when you move these tomatoes to larger pots. Personally I like to use organic fertilizers and have used this one with success in the past.
Aphids are the most common pest that bother indoor plants and I don't see any sign of them in your photos.