Good job on the cuttings.
How much root mass do you have? and How old are the cuttings?
If you have a good amount of root mass and they are getting enough light they may need a little fertilizer. I use a very weak Miracle Grow mix, 1/2 teaspoon to 1 gallon water of standard MG garden fertilizer.
Water with fresh water first and then with fertilizer, but only if you have good roots. The cuttings will also grow rapidly if it is warm. I have been keeping my cuttings in a south facing window in an unheated room and they are growing slow, but healthy.
If you can get a few figs and leaves from the mother tree this year, you may be able to identify the variety.
Good Luck.