How can you tell when you've encountered a themed pet in the festival zones? My task log says I encountered one and I'm wondering if I just didn't notice or if I missed a notification in the log or something.

When you encounter a themed pet, in your battle log, it'll say it's a Rare Enemy. And in the battle, the pet will have a name, such as Goldfinch Aurleon. It'll be of at least Rare Rarity(Blue stars), though it can also be Epic(Purple stars), Legendary(Yellow/Orange/Gold stars), or Mythical(Red stars).

But, to encounter a themed pet in the fest zone, it doesn't have to just be through battle. If you encounter an egg in the fest zone(All eggs are themed in the fest zone), it'll also count for the themed task. So if you found a themed egg, that would have counted as well.

Also, during Spring Fest, you can encounter non-themed pets, that'll also say Rare Enemy. These are Spring Blossom Pets(They have the restricted trait, Spring Blossoms), and only pop up during the Shared Garden events(When there's a timer in the Zone Progression box with a Species name).
When these events are active, you can encounter Spring Blossom pets of the same species that are in that box. These events also increase themed rates, and gives you the chance to encounter Fairies. Like with themed pets, the Spring Blossom pets say Rare Enemy in your battle log, and will say something like Spring Blossoms Aeridini. These pets are guaranteed to be Epic or Legendary rarity. They can't be anything less, and they can't be Mythical either.

I hope this explanation helps.^^

There is also a special themed pet you can encounter in the Egg Maze. If you pay 400 diamonds to do the Mythic Egg hunt in the Egg Maze, you will have a chance of encountering a Lagoon Nymph Nephini. In you battle log, it will say Legendary Enemy when encountered. Unlike regular themed pets, the Lagoon Nymph Nephini can also be found as a Green Star(uncommon) and only carry one trait. That is because they have Restricted Traits. Restricted Traits are traits that cannot be found normally on Themed or Wild Nephinis.