I'm really scared they cut my cuticles? Help?

At a nail salon I went to, it seemed really unhygenic. Like when he was cutting nails it was flying all over the place, on his shirt, and the manucirist didn't care.

He softened my cuticles with soap, and then actually cut them with a cuticle cutter. I was afraid, but there was no bleeding so I thought he knew what he was doing.

Now I'm scared, apparently you're not supposed to do that. And cna I get infected?
I'm really scared they cut my cuticles? Help?
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