If I didn’t claim my children as dependents, why is their fathers taxes getting rejected for him claiming them?

Either one of 2 things happened.

Most likely, you still had them on your tax return, even though you didn't claim them, therefore, their social security numbers have already been submitted with a return. If you go back into your return and see their names anywhere, or if you received the earned income tax credit or any other credits for them, this is what happened.  If this is the case you will need to Amend Your Return and take them off of it completely. 

 The Amended forms are expected to be available in TurboTax Online around February 7th.   It can take up to 16 weeks for the IRS to process an amended return.  This means he will either need to file an extension or print and mail his return if he wants to claim the kids this year. 

Remember, when you are filing the Amended Return, you will need to print and mail the 1040X as it is NOT able to be e-filed.

Second, a much less likely scenario is that someone else used their SSN accidentally or intentionally.  You would need to contact the IRS to see if that is the case.