It uses a floater like this, so I think I am OK and don't even need the backflow device
Sorry, no. The opposite is true, and in fact a cheaper check valve won't do.
Unlike a toilet setup, your pool's float valve releases water under the surface. So it needs a backflow preventer (BFP) upstream. A toilet's float valve releases water though a set of tubes that creates an air gap between the supply water and the toilet water. No such air gap exists in your autofill vault. The white tube that kind'a looks like the tube you'd find in a toilet tank is your overflow outlet.
And because your autofill flow valve is under constant pressure, so too would be the backflow preventer. Which is why you can't use a cheap one, or a sprinkler valve. A cheap one can fail and because it's all sealed up, with no way to test it, you'll never know if it's working or not (well, not until pool water backflows into your drinking water). And a sprinkler valve won't do because they are not rated to have constant pressure on the outlet side, only on the inlet side, so it too will eventually fail and you might not notice that either.
You need a
pressure vacuum breaker (a type of BFP), like the one I have. Pressure rated, solid brass, sturdy, reliable and testable:
Zurn 34-720A Wilkins Pressure Vacuum Breaker 3/4-Inch Assembly: Amazon.com: Industrial & Scientific
www.amazon.com
We've strayed more than a bit from the original topic of this thread. If you want to know more about this, you can PM me or start your own thread and then let me know where it is...