Time Complexity: Intuition for Recursive Algorithm
Based on the code you show there, your intuition is right.

However, it looks like there is a typo in the code and the next-to-last line should have been

  q = max(q, p[i] + CutRod(p, n-i))


i.e., n-i rather than n-1.  Try to work through a proof of correctness, or through a few examples, to see why I say that.  The running time analysis they show is for the corrected code, rather than the code with the typo, and then once you make that correction to the code, the recurrence relation they provide is correct.