I've seen a lot of problems like this in every kind of game that has some kind of RL money charge to the game, it is mostly the companies fault due to the fact that their server was probly lagging with a lot of people purchasing RP and with the lag it would / Accept the offer, or in your case a purchase. I would send an email telling Riot that this happened with a picture with the double purchase on it and also call your bank notifying them that this was a false purchase and only recieved 1 of the purchases after you get a reply from Riot.
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Thank you for all the input.