In NJ and the other States with which I am familiar, there is no set time limit for one County to come and get him from another County, although it usually done within a relatively short time period since the purpose is to get the person back in front of the judge in the requesting County, in regards to the failure to comply with the sentence imposed by the Court (the outstanding fines). Typically, I would expect this to occur in a week or two at most, depending on Court schedules and personnel availability. Obviously, if he has a lawyer in the Counties seeking him, the lawyer can make specific inquiries about when the transfer will take place, or make other applications to the Courts for his release if the transfers do not take place. Good luck.
DISCLAIMER I do not practice law in your State. This answer is provided for informational purposes only. This answer does not constitute legal advice, create an attorney-client relationship, or constitute attorney advertising.