that is how it works in civ5 as well. if you dont have open borders from them your missionary takes 25% damage per turn. great prophets are not affected by this.
the strategy is to try not to end your turn with the missionary in enemy borders. ideally you stop just outside their borders then in one turn run up to the city and pop it. it'll lose power (50% iirc) from use, it'll lose an additional 25% of its total power from being in enemy borders, then you can move it out to neutral ground. now you have a weakened missionary you can still use again.
or just get open borders.