You only need to potion the starter monsters and a few which you get on the islands that become a higher grade of monster when you evolve them. If you potion them before then they take lower quality potions. For everything else it doesn’t matter whether you potion them before or after evolving.
Here’s a guide you might find very useful to read: KD's New Players Guide
Here’s one that goes in-depth explaining everything about bonus potions: KD's Bonus Potions and Entrance Speed guide