This summary is not the rule. The rule text controls.
If you are a witness traveling from another state to testify in an Oklahoma court case, this rule protects you while you are here. As long as you are following a court order that tells you to come testify, you cannot be arrested in Oklahoma for something you did before you arrived. You also cannot be served with civil or criminal papers for those past actions while you are here under that order.
This protection exists so witnesses are not afraid to show up and testify. Without it, someone might avoid coming to court because they fear getting arrested or sued the moment they cross the state line. The rule makes sure people can travel to Oklahoma, give their testimony, and leave without worrying about unrelated legal trouble catching up with them during that trip.
This protection only covers things that happened before the witness arrived under the court order. It does not shield someone from arrest or legal action for anything they do while they are actually in Oklahoma.