Reiteration mashing

I did an Imperial stout in the weekend and mashed two lots of 5kg grain to get the required abv. Week 74 Grainfather blog tells me to

https://www.grainfather.com/blog/week-74-reiterated-mashing/

"Start with your initial grain bill and the necessary volume of mash water. You will be mashing the same grist each time you mash. Say you start with 5.5 kg (12 lb) of grain, you will need 18.1 L (4.8 US Gal) of mash water and 14.1 L (3.7 US Gal) of sparge water."

I was left with too much water after this step which I only realised as I had poured most of the second batch of grains in. As I got all the grain in the basket the water level was way too high and flowing out the  basket lifting holes. The pump then got clogged and blew a hose. Have I read this article wrong? Clearly you should start the second mash with 17 litres?