The reason why is this…
If you have another shut-off valve after the anti-siphon valve, then the water on the downstream side of the anti-siphon valve will stay pressurized even when the anti-siphon valve is closed. This water pressure holds the little air vent in the closed position so it can’t let in air, and therefore the siphon effect is not broken. This means the anti-siphon part of the valve will not work. Even worse, when the little vent is held closed for days at a time due to the constant downstream pressure, it eventually just sticks in the closed position. Then even if the pressure drops the anti-siphon won’t work.
You really should either replace all 6 valves with Anti-siphon models and remove the “master” valve, or install a Zurn/Wilkins or Febco backflow preventer. The Febco units are more compact than the Zurn/Wilkins if space is an issue.