It will be up to the local prosecutor in Minnesota. If they want to, they can ask Californian to arrest and hold him for transport.
Whether extradition occurs is entirely up to MN. It would be my guess that MN has already made that decision when the warrant was indexed in the NCIC database. That indexing will indicate whether they intend to extradite. If he is stopped for any reason in CA and a check is made for outstanding warrants MN's desire to extradite will prompt the CA law enforcement to hold him in the local jail and notify the authorities in MN of his apprehension. MN would then institute extradition proceedings. It's unlikely that any specific efforts will be undertaken in CA to locate him unless MN authorities have some information as to his likely location. If that were the case MN would notify CA authorities in that area of their beliefs and some effort to followup would likely occur. I would suggest that you not post further information about the case on the Internet. I would also highly recommend that he be in contact with MN legal counsel to discuss the best course of action. Living life with the constant threat of apprehension is not appealing for most people and making arrangements to voluntarily return to MN to face the charges would likely be viewed with favor there. At this point MN has evidence it considers sufficient to convict your brother. The more time that passes the harder it will be for defense counsel to assemble evidence favorable to your brother. I personally see no longterm upside to remaining at "liberty" with an outstanding warrant for his arrest.
On those charges there is a good chance they will extradite him, but it is ultimately up to the prosecuting office to make that determination.