Hayley will bring her own Pokémon to the Ranch, 1 species a day, with a max of 5 Pokémon being brought in a day of a single species. The Pokémon she brings are completely random but there is a way to dictate what she brings. If you are interested in doing the Trades for Hayley's special Pokémon you will want to dictate what she brings into the Ranch because the only to get those trades is by first having the Pokémon you want to trade for in the Ranch.
To dictate what she will bring to the Ranch simply say "No" to Hayley's ideas twice. After that she will decide what is best to bring to the Ranch and the chances are that it is 1 of the 20 Pokémon she will trade to you.
Before leaving the Ranch for the first time of the day, she will give you a hint and ask if you would like to see that Pokémon come to the Ranch. If you select "No" she will make another offer. When declining this second offer she will bring a Pokémon of her choice and you won't get to read the hint. You still see the painfully obvious "blackout" picture that is shown when you accept one of the first two offers.
Once your Ranch reaches level 20 Hayley's Pokémon stop counting toward the general population and once your Pokémon are great enough in number that hers no longer have room, she will remove her Pokémon from the Ranch's general roam area and place them in the barn which she expands at level 20..