In the app it says each expansion (labyrinth of ruin, manor of ravens etc) grants one extra side quest to be played in the campaigns.

But I've noticed that there has been more than 1 side quest I've seen that's focused on an expansion monster or used tiles from the expansion? (I have shadows of nerekhall)

So does each expansion give you more than just one extra side quest in addition to the base game quests?

There is one main story quest that uses a single tile from the SoN expansion if it is in your collection. Other than that there is only one side quest that features tiles from that expansion. You can encounter monsters from any expansion in any of the quests based upon the use of open monster groups. The app does a great job of using the monsters from the expansions. I have both big box expansions 1 small box and one H&M pack and I've seen every monster from my collection in the various campaigns I am playing.