Pokemon Island is off the coast of Kanto.
That would explain why Prof. Oak is there.
Pokemon Island is Faraway Island from Pokemon Emerald.
Hence why Mew lives there. Faraway Island could be fairly close to Kanto as in the above though, as it's only far away from Hoenn.
The events of Pokemon Snap take place before RBY/FRLG.
Specifically, the game explains how Mew was first discovered. Subsequent researchers managed to capture it and bring it to Cinnabar Island.
Also, in RBY/FRLG, the Legendary Birds are just randomly hanging around, unlike most later games where the legendaries have to be released by the player or the villains as part of the game's plot. The birds are released in Snap.