Even if Youkai Watch isn't part of the FF Universe yet, it will be soon.

I'm sure they will find a way through quests and dialogue to add these characters and items into the Final Fantasy world and lore.

I very much doubt they will simply appear out of thin air with no explanation.
If someone is interested in lore, I think they should read the dialogue of the quests to understand why these weapons and minions appeared in the game.

When the Valentine's Day event was held, I don't think people complained the Valentine's Day (named Valentione's Day or something like that) wasn't part of the FF Universive. But it became a part of it.

The same is true for many seasonable events. Take the New Year's event and Easter event as another example.
Keep in mind that Japanese do not celebrate Easter, and really know nothing about it, yet there was an Easter Event with eggs and stuff.

Youkai watch is very popular in Japan. Many people are very excited about it.