I'm running Notation Software first.
But then any option to open a file creates that effect, via menu bar, dragging a file or choosing from the options page history - during the first start.
Never had issues with the midi drivers with other software. What kind of problem do you think of? But I've boiled down the used midi ports in Composer now to just the ones I need and see...
BTW, I now have the full version and it behaves the same.
I wished I could find out what is different with the second start of Composer. Without understanding this I think we have no chance to fix the issue...