quantum field theory - Using Wick Rotation to calculate Generating Function in Minkowski Space

The question arises when I'm reading over the section "3.3.1 Minkowski Space" in page 16-17 in the following link: https://www-thphys.physics.ox.ac.uk/people/JohnCardy/qft/qftcomplete.pdf

It is discussing the technique of using Wick Rotation to calculate the generating function in Minkowski space.

It mentioned that simply inserting $τ=it$ into the results of the generating function in Euclidean space (i.e. imaginary time) provides the generating function in Minkowski space.

However, on top of page 17, it mentioned that I also have to let $p_0 \to ip_0$ as well. Why do I have to do this as well? How is that related to defining $τ=it$ and making a Wick Rotation?