This is just how multiple value dropdowns work. You don't have to click on the arrow again, you can click anywhere away from the filter menu and it minimises.
You could post this to the ideas forum for Tableau in implement in a future release. Ideas
I hope this is useful.
I there some kind of setting that we can change for auto minimization after apply button is clicked?
No, I'm afraid that isn't an option. However, as I mentioned you could suggest that as an idea for the development team to look into adding.