Typical methods for using spiral mixer seem to be different in the US vs Italy.
In the US, the method pioneered by Tom Lehman is quite popular - it works very well IMHO because the majority of pizza operators in the US use hydrations of 65% or lower and make medium to large batches of dough. Under these conditions, going water in first works well and reduces total mixing time as Tom mentioned. Also, and I'm only guessing here, this method might work better for older or poor performing mixers which have a tendency to leave some of the flour on the bottom of the bowl if you put flour first. Planetary mixers like KitchenAid have this problem so bread makers like Richard Bertinet recommend going water in first to avoid the issue. Modern spirals really don't have this issue, but I imagine some older or lower end spirals might. If you start with the water, there is practically no chance of any flour remaining on the bottom after mixing.
In Italy, hydrations for pizza dough can go all the way to 80%+ for styles like Pizza in Pala or Pizza in Teglia. For higher hydrations, it makes more sense to start with the flour and slowly add water to the flour, waiting for the water to be absorbed before adding more. If you put 80% hydration of water in first, you will end up with a pancake batter and the dough will never stiffen - Italians call this "non-legato" (not tied). The idea here is to build the gluten at 55-60% hydration and then add water slowly, while maintaining the already built gluten network. I think that the flour first method is most popular in Italy among other reasons because it works for all styles, starting with the 55% hydration for Tonda Romana all the way to 80%+ hydrations of Pizza in Teglia. Another reason is that the modern method is to use a fixed amount of flour such as 1000g but adjusting the water as needed. Therefore, it makes sense to start by putting the flour in first because it is a constant.
Both methods work, and the batch size and specific spiral mixer also play a role. Some mixers work better for water in first - the pumpkin forms sooner. Some spiral mixers do not work well with water in first with small batches. I would try both methods and see which works better for your mixer and your specific dough.