Please explain what you mean by "filing twice." What did you do?
It is not possible for two tax returns to be accepted by the IRS for the same Social Security number. So at least one of the returns you tried to file will be rejected. Did you also e-file the return you prepared using TurboTax? If so, wait for the email that tells you if the return was accepted or rejected.
Did you enter the same exact information on both tax returns--the one with Tax Act and with TT? If you used the same information the results should have been the same.
If the first return was accepted that is the one that will be processed. You cannot do anything about the rejected return you prepared using TurboTax. But you must have entered something differently. Tax preparation software --no matter what company provided it--- has to comply with all of the tax laws. The same data should yield the same results. Wait and see what the IRS does with your Tax Act return. Good luck.