Purple on the leaves could be indicative of one of three things:
- Phosphorus deficiency. Cold temperatures can make this worse.
- A variety that is supposed to get anthocyanin on its leaves. In this case, there's no problem.
- Sulfur deficiency (most people might not think this makes the leaves look purple, but I kind of think they look a little purple and translucent—not as purple as with the other two items listed here, though); your plant doesn't look like it has sulfur deficiency, however.
Yellowing (if the veins are yellow, too, and it's not just the edges of the leaves that are yellow) is probably indicative of nitrogen deficiency. If it's just the edges of the leaves that are yellowing, that's usually potassium deficiency. Yellowing leaves with green veins is usually something like magnesium deficiency. Overwatering can cause yellowing (and a host of other issues), but it doesn't cause purple leaves.
Too much of certain nutrients or soil amendments can also cause yellowing, sometimes (e.g. too much wood ash).
It sounds like you probably used seed-starting mix (which is what you should have done) and the plant finally needs fertilizing. However, it shouldn't be dying if that's the case. If it's dying, something else is wrong. I'm guessing something may be off about the soil. It sounds like the plants are getting plenty of light, which is great. The plant in the picture doesn't look like it's dying, though.
Just water the tomatoes when the soil dries out on top. Most people probably water their pre-transplant tomatoes every two to three days or so, if they're in those plastic cells. If they're in larger/smaller containers, and depending on the soil, things may be different.
