Copy parameter object before setting in subset_tunables

[DhairyaLGandhi]

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

closes #3921

cc @AayushSabharwal @SebastianM-C @ChrisRackauckas

Add any other context about the problem here.

[SebastianM-C]

This fixes my MWE, thanks!
That could be added as a test to ensure this does not regress.