This summary is not the rule. The rule text controls.
If someone commits a felony in another state, or is convicted and skips out on their sentence, and then they run to Louisiana, the governor is required to have them arrested here. Once caught, the governor must hand that person over to the state where the crime happened, so they can face charges or serve their sentence.
This means Louisiana will not act as a safe hiding spot for people wanted in other states. The governor does not get to pick and choose whether to cooperate. As long as the legal paperwork and process required by this section of the law are followed, sending the person back is treated as something the governor must do, not just something the governor may choose to do.
For a person facing extradition, this rule explains why they can be picked up in Louisiana even though their alleged crime happened somewhere else. It also shows that being in a different state does not protect someone from facing charges or punishment tied to another state's court system.