Tenuiflora and most of the commonly discussed acacias thrive actually quite well under T5 fluorescents during the seedling stage. It's true that, in order to maximize growth, sunlight is the best as long as the temperature is not too cold (nor extremely dry and hot when they are young) but they can do fine under lights the first months. T5s can be kept at a few inches from the seedlings to make the best out of them.
About moving them outdoors, unless you leave in a very warm zone, I'd wait until spring. The lack of light can be just a growth limitation, but low winter temperatures will kill tenuiflora seedlings, or at least stunt their growth badly. I have germinated them indoors in late fall under T4 and T5 fluorescents, and moved them outside in march (southern Europe) with nice results. Actually the first challenge was getting them to survive the next winter outside.
As for the other conditions indoor, ideally warm-ish temperatures, I'd say 40%-70% relative humidity, and good drainage in the soil. Some air flow is good because it makes them exercise, thickening the stem and spreading stronger roots, so throw in a little fan if you can. Water not too frequently, don't let the soil dry out completely in the seedling stage but the older they get, the longer you can wait between waterings without stressing them out. And keep checking the leaves for nutrient deficiencies.
Keep us posted,
Mandrake