"Turning yourself in" is just a procedural move in this case since Perry is not going to be taken into custody. He was charged so he has to be formally booked and photographed, but he's not going to remain in the jail and it doesn't imply admission of guilt. There may be some restrictions on him traveling or leaving the country, depending on whether the judge thinks he's a flight risk.
Oh I see, thank you for clarifying. Nevertheless, transferring powers to Dewhurst temporarily might look like responsible governance. It pretty much allows Perry to continue governing from the back while showing that he's cooperative with the investigation and is not an abuser of power.