I have mixed feelings about this, to be honest. My most recent labor was about 18 hours long-probably in reality a bit longer. I wanted to get in the tub several hours into labor but my midwife wanted me to wait til I was dilated to a 6 first because it can slow labor down. She is right that in can slow labor but at the same time you need to be comfortable. I had a very putsy, but managable labor. I knew exactly which positions gave me the strongest, most effective contractions but they were also the most painful and unbearable ones. So for most of my labor I chose the comfortable positions that didn't quite get me the most effective contractions, but things were still happening. Maybe I am lazy or scared of pain but I would prefer a managable long labor over an unbearable short one. All that to say, I did wait til I was dilated to a 6 before getting into the pool. However if you choose not to get vaginal exams during labor, how will you really know? So I would personally just do whatever you want! If you want to get into that pool 10 minutes into labor, then you should. Maybe that is bad advice but that is what I would do.
Oh wait, that wasn't even your original question.
We started filling up the pool as soon as I felt the desire to get into the pool. It took awhile to fill up.