I notice you've achieved getting poults from them, however I still thought I would add a little general information.

Domestic turkeys include breeds too large to mate naturally.
When she shrieks, it's often because she's hurt. It has nothing to do with a successful mating. But often a clumsy male takes that long to mate that she's out of breath and in pain by the time he manages. A good tom is one who can get the job done quickly. Some just sit on top of her, crushing her. These ones are often responsible for dead hens. Just because she doesn't seem outwardly injured doesn't mean he didn't just crack a rib. The shriek you mentioned can occur at any time but with most of my turkey's successful matings, it never occurs.
It's not his nails. It's most likely either his weight or a previous injury sustained while trying to mate that's discouraged her. Even experienced hens are sometimes averse to having to go through the crushing. Some folks solve this by only breeding the equivalent of teenage toms, not at their adult weight, while others buy saddles. Commercial breeders use either saddles or artificial insemination for the most part. I breed bantam turkeys with full size ones, so the females cope better with even mature toms.
If she displayed at him, she was most likely hurt and angry. The normal response to a successful mating is to shake her feathers and walk off.
The shrieking does not indicate penetration, because turkeys have no penis. No penetration occurs. If they didn't reach the point where his tail was under hers, no mating occurred. The longer he stomps on her and fails to achieve mating, the more likely he is to kill her in the attempt. However young males are often quite clumsy, and on the bright side he's not at his full weight yet.
It is normal for male and female poults to take turns displaying at one another. One will crouch, the other will mount, they mate like adults, but of course without viable sperm, and then the one that played hen will get up and play male, and the one that played male will sit down and play hen, and so it goes. Sex role play is normal to turkeys and chickens with any serious instincts retained from their ancestors.