Ok, a couple of quick points:

1.) Your seedlings are very young have no need for fertilizer and probably won't even benefit from it in any meaningful way for a few weeks. In fact, fertilizing now will likely do more harm than good.
2.) As far as watering, keep them moist, but not wet. If the medium (in your case Oasis Cubes) still feels wet, they are probably retaining too much water for the liking of the seedlings.
3.) Your lights should be a lot closer to the plants, 6" is way too much, imo. In general, the light should be about 2" from the leaves if you're using shop light style UV lighting.

By the way, all that being said, all of the tomato seedlings you have pictured look perfectly fine, in my opinion, I'm not quite sure why you think there is a problem there. They just look like normal young seedlings, is there something I'm missing?

Definitely not damp off. Actually they look like pretty healthy little newly sprouted tomatoes, as Homgardenpa said. They are leaning reaching for the light, or from the fan blowing constantly on them, but that is normal. 6" is a bit far to have the light, they may wind up leggy because of it.

There is no reason to fertlize seedlings, but it sounds like your solution may be so weak that it isn't a problem, though I did see a couple of crispy edges, but that looked like seed coat issues rather than fertilizer burn.

What makes you think they are sick?

Betsy

Agree with the others that basically they look ok, not great, but ok. But you do need to lay off the fertilizer bit completely. You can dilute feed after they develop their second set of true leaves if you wish but not before.

When you compare your plants in the peat pellets to these and see the differences then it's clearly ferticube related. One of the issues with both, and especially with ferticubes, is that they surface-dry so quickly. Makes it look like they need watering when they don't. So they both tend to get way over-watered.

Next year consider using the recommended alternative to both - seed starting mix in small containers - for best results.

Now with the ferticubes - do you plan to grow these hydroponically? If not you will discover that ferticubes don't transplant into soil at all well. They aren't intended to. So soak them well before transplanting and bury them deeply into a good loose soil-less mix so the roots can get around and out of the core cube easily for best results.

Dave