That's all you need to do. The upgraded products from chickens are based off of winning the chicken festival, and the upgraded products for livestock are from visiting Animal Land for about 50 hours in-game.
Technically it is less than an exact 50 hours because you get credit for just simply having your animals go there. You could just go to Animal Land 50 times, not spend any time there at all, and still earn the upgraded animal products.
I was gonna ask about this too kind of. Because I couldn't win the cow festival even though my cow is producing 5x 5 star milk and reached the bigger size. Talked to villagers after losing and they kept saying I should bring them to animal land, and I wondered if I really should. Guess I should *sigh*