Also for your question, its only the characters unlocks that carry over, not any levels/progression for the characters
For the OP, I’m going to sleep soon so I’m gonna guess what your problem is.
The levels in the Hunters Quest app only affect there in app strength and your progression for a specific badge for that character when they reach 30
The progression from the app is having the stars 50% completed if you rank them up using the mastery points awarded as loot from the app.
At the home page of the app click on ‘Connect to EVOLVE’
You should see all 12 of the hunters.
Click on whatever character you want progression for.
This will take you to a page where it has level 1/2/3 for the hunters tools
Use the mastery points to unlock these
You now have 50% of that weapons 1/2/3 star