I noticed that happens when zapping, but are there other ways?

Random event will increase a random pet's TC sometimes.

Magical Keepsake Box Gives a pet of your choice 1-3 treasure slots at random.

There's another way but I really know nothing about the item.

Increases your pets Treasure Chest at least 10 spaces costs around 6 mil sP or 150CSC

Ah yes that's it, thanks for clarifying.

Oh neat, thank you!

There is one more way. After 2 years (and every year thereafter) you get a loyalty totem and one of the choices is to increase pet TCs.

Oh wow, that's awesome! Thank you!