Why is the circulation around a centrifugal impeller blade tip the opposite to a wing tip?
I think what's confusing you is that the text book is using the term circulation to describe speed relative to the average airflow, not actual circulation around the blade.

There's still a black arrow pointing outwards on the high pressure side of the blade - no air is travelling inwards.

However if you look at the difference between actual speed and the average speed, it's negative on the high pressure side and positive on the low pressure side.

I don't fully understand the theory, but I think you're supposed to imagine the surface of the aerofoil (or an infinitely thin layer of air next to it) to be circulating, and causing the velocity gradients.

Wikipedia says:

Circulation is often used in computational fluid dynamics as an intermediate variable to calculate forces on an airfoil or other body.