He isn't in Pal Park, he's in Eterna City
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He will apear in Eterna city in the house right from the gym
After you obtain the National Pokédex and visited the Pal Park, Professor Oak appears in the southernmost house in Eterna City.
pretty much go wherever. go to pal park and everything. the object is to fill up the national dex
He gives you an up-grade after you go to pal park (no you don't have to migrate) and he's in the little house at the southernmost point of Eterna city
After you get a sight of all 210 Pokemon, go back to the lab of Rowan and speak to Professor Rowan. Follow Oak to the new Pal Park, then go to the house near the Eternia Gym. Oak will then give you an upgrade