Robert,
What they will do is once you are approved for your children they will deduct their benefits from your monthly benefit amount. The overpayment will start if lets say you were receiving 700 a month since 1/10 then your children benefits are approved from 1/10 as well. If your children benefits are lets say 300 a month basically they will calculate they should have only been paying you 400 a month instead of the 700 a month then multiply the difference from 1/10 to the present month you receive benefits. They did not take my children's back pay however they calculated an prorated overpayment that somehow was more than what I received for their backpay. Very confusing but it was in my policy and you will have to apply for your children benefits if it is in your policy as well. I wish you luck.