Getting fillings half way through Invisalign treatment.

I recently visited a dentist and it turns out I have 5 cavities that need filling. I intend to address this problem sooner rather than later, so waiting till after my invisalign treatment ends in November is out of the question. I've read that the fillings will result in the trays not fitting properly so will my teeth be rescanned and new trays be made? And how long is this likely to take? I'm worried that my teeth will shift back since I won't have trays that will fit while I wait for new ones.