Seedlings need bright light, heat, oxygen in the roots, and potassium and nitrogen.
With grow lights, leave them on 14 hours a day and keep them as close as possible to the plants without burning them. I keep mine within an inch of the tallest.
Oxygen: too frequent / too much watering or poorly draining soil will prevent the roots from absorbing oxygen. Plants use this oxygen, combined with co2 from the air and energy from light to construct carbohydrates. It is vital. Therefore, use a commercial substrate or soil meant specifically for seedlings, and don't water too much.
Temperature: tobacco grows best between 20 and 26, so a cooler garage or basement is less than ideal. Keep in mind, especially if you live in a dry area, that evaporation of water from the soil drops the temperature of it significantly. Stick a thermometer in the soil to see. A seedling heating mat will help. Tenting the grow trays with plastic will help, insulation underneath will help. Humidifying the grow room will help in multiple ways; one, by preventing the cooling evaporation as well as giving you the confidence to avoid over-watering.
As for nutrients, if you use a commercial seed starter soil, there ought to be enough nutrients for 8weeks. If it goes beyond that, or if you are using peat pellets instead of soil, you may need to fertilize. I personally use peat pellets in larger cells that are filled with dirt, so when the roots get beyond the pellet, they start getting the higher concentration of nutrients that they need as bigger plants. Also, water from below. Watering from above leaches soluble nutrients out of the soil.
Another thing is, never fertilize or over-water (see the theme?) plants that are under stress. Patience is best. Aside from that, the one trick I offer is, 2 weeks before planting outside, dissolve half an aspirin in 4L of water and use that for watering, or spray it on the leaves. This promotes root growth and enables certain survival mechanisms that will make it more hardy during transplant.
Oh, and when the seedlings are starting to get a little bigger, give them a haircut. Cut off the most distal third /the tip of the largest leaf on every plant. This also promotes root growth and strengthens the plant's immune system.
Good luck man