I teach multiple ways, and what you describe does not sound like any of them.
I learned this about 10 years ago from a very sharp guy.
Trigger finger straight
Remove support hand from AK and access new magazine. Grab mag at about mid body.
Move the fresh magazine along the bottom of the trigger guard, sweeping forward- it will activate the mag release, and push the old magazine out of the mag well.
Rotate your support hand and insert fresh mag into the mag well.
Hope this helps.