That would be up to the individual jurisdiction's District Attorney's office.
I have arrested individuals on out-of-state warrants and the originating agency then sent us an official communication requesting that the person be held pending pickup. In two cases the warrants were out of California and in one case it was out of Massachusetts.
In the MA case two detectives drove down to pick the person up within a few hours. In the case of CA, after I lodged the prisoners I never followed up to confirm that they were, in fact, picked up. In one case it was a parole violation, in another it was three fairly serious felony weapons/drug charges.