I have Y and Alpha Sapphire, and the events are compatible on all gen 6 games, so what's stopping me from going to get 2 codes for Mew, one for each game, or downloading 2 Jirachis over both games?
If you get a code, then I suppose it's up to the store employees whether or not you get 1 per game. However, if it's just a WiFi download, you are absolutely able to get one event Pokémon per game. I got two Genesects and two of each Shiny Sinnoh dragons on my White and White 2 games via WiFi download.