Originally Posted by Fat Kikuichimonji
I had entirely forgotten the function that automatically sends Pokemon to Bill's PC when Red/Gold is carrying six Pokemon. It's safe to assume that being able to send a Pokemon to Bill's PC from anywhere in the world is a function exclusive to Pokemon immediately after being caught with a Pokeball, because (IIRC) all situations in which the main character is given a Pokemon require that he have fewer than 6 Pokemon in his party. The only example I can think of is Tyrogue from second gen; I don't recall whether Eevee is the same way.
In RBY they're sent straight to the PC
This happens with Hitmonchan/lee, Eevee and Lapras