Taper Crimping. Unlike a roll crimp, a taper crimp does not leave a radiused edge on the case mouth. A taper crimp simply flattens out the 'belling' that was previously done by the expander die, and squeezes the case mouth tightly against (but still mostly parallel to) the sides of the bullet.
So yes it does put tension on the bullet. Try simply loading one round without crimping and see what happens. The bullet will move. Now put the bullet into the loader again and do a crimp and remove it. The bullet will no longer move if the crimp is correct.
The Full length sizing die sizes the whole case back to spec. Once this is done the primer is expelled and a new primer can be installed. Once this has been acomplished the neck of the case is belled and powder is put in. From there a bullet is seated in the case and from there the the crimp die removes the belled case neck and crimps the bullet.
This is the correct explanation.