When I got my first Tower Garden in 2010, I tried growing inside the tomato seeds that came with the Tower. They were leggy (cue the “Attack of the Killer Tomatoes” music here) and attracted insects. I switched to lettuces and did much better, but never investigated why the tomatoes didn't do well. Last year I wanted to try tomatoes indoors again. This time I asked questions and did some investigation on my own. I discovered that it's possible to grow tomatoes indoors, but they won't do near as well as growing outdoors. There are 2 reasons why.
We have to mimic inside what God designed perfectly to grow flowering fruits and vegetables outside.
Bees pollinate your flowers which produces the fruit and vegetables. Indoors you'll need to pollinate the flowers yourself. That trick can be learned – and with the declining bee population, it isn't a bad skill for outdoor gardeners to know.
But the most difficult problem is the light spectrum. For a plant to flower and produce fruit, it needs light in the low end of the spectrum—around 3,000 Kelvin. For a plant to produce nice leaves it needs a light in the high end of the spectrum—around 6,000 Kelvin. So tomatoes, for example, need a 6,000 Kelvin light during the leafy part of growth. Then they need a 3,000 Kelvin spectrum to produce the flowers and fruit.
Outside, the tomato gets this as the summer progresses. During the heat of the summer, the light is on the higher end of the spectrum helping the plant to produce nice leaves. As the summer progresses and the earth tilts, the light switches to the lower end of the spectrum helping the tomato to produce the flowers and fruit. (Here's more than you probably ever want to know about light spectrum. http://suburbanvegetablegardening.com/lighting-an-indoor-garden/)
The lights that come with the Tower Garden are in the 6,500 Kelvin range. This spectrum of light produces great leafy greens, but won't help produce the flowers.
Could you switch bulbs mid-way through the growing cycle of your tomato plant? There are professional growers that do. So if you try and get it to work, let me know.