I think this question is founded on an incorrect premise. I don't believe it is anywhere stated that Dumbledore performed the Fidelius Charm. What is stated in Chapter Ten of Prisoner of Azkaban* is:
Dumbledore told them that their best chance was the Fidelius Charm."
I remember him offering to be the Potters' Secret-Keeper himself.
It seems that Dumbledore advised the Potters to use the Fidelius Charm and offered to be the Secret-Keeper, and they accepted his advice but turned down his offer.
Later in Chapter Nineteen Sirius says:
"I persuaded Lily and James to change to Peter at the last moment, persuaded them to use him as Secret-Keeper instead of me....
Presumably Dumbledore was simply never told about the switch. Indeed, Dumbledore explicitly states in Chapter Twenty-One that he gave evidence that Sirius had been the Secret-Keeper, which he surely would not have done had he known that Sirius had not been the Secret-Keeper:
I myself gave evidence to the Ministry that Sirius had been the Potters' Secret-Keeper."