What is an IDC punchdown tool used for?

It seats an insulated conductor into an insulation-displacement contact so the contact cuts through the insulation and makes the electrical connection. On a cutting termination, it also trims the excess conductor at the same operation.

Use it on the IDC style it is designed for. The tool is there to make a controlled termination, not to provide a more elaborate way of pushing wire into any slot that happens to be nearby.