Is it effective to tweak the last aligner to make final adjustments to the teeth? Will this produce results?

I hesitate to judge another dentist's treatment plan, not knowing everything about the case.  There are times where tweaking existing aligners can be a great approach.  If the corrections are relatively minor, tweaking an existing aligner may save you time waiting for Invisalign to manufacture more aligners.  It may also save you expense if you are responsible for more aligners than Align allows you.  I don't know if it was the best approach in your case or not, not knowing all the ins and outs of your situation.  It seems likely to me that, IF you are wearing your aligners faithfully, you may have played out the usefulness of the last aligner by this next appointment, and new aligners may be necessary to continue from there.  While no one is perfect, I would trust that your dentist is doing his or her best until it is extremely clear otherwise.

Why not ask the dentist to make a "mid-course correction" or use refinement aligners, which can be ordered from Invisalign? There might be an additional charge. Aligners lose their "rigidity" after wearing for a few weeks and become less effective.