Magnetic float switch + relay setup to control a water pump
Your title and post mention a &quot;flow sensor&quot;. Your diagram shows a float switch which is something completely different. That technology will be at least a hundred years old - so hardly &quot;state of the art&quot; so I'm not sure what point you're trying to make there. You also stated, &quot;But when the water level in the pump goes down, ...&quot; and this should probably be &quot;when the water level in the tank goes down, ...&quot;.
The diagram you are using is for a 2-level-sensor arrangement using both minimum and maximum level sensors. Since you have only one level sensor that's the wrong diagram to use. You're looking for the diagram for one minimum level sensor and running the device in &quot;fill function&quot; mode.

Figure 1 (the fourth on page 12 of the datasheet) shows that the tank minimum level input is monitored and when it turns on the relay output will turn on after a time delay, Tr.
Setup:

Set the top switch anti-clockwise for fill mode.
I suspect the sensitivity adjustment is for an analog sensor. Since you're using a switch the setting may not matter. Adjust until you get it to work.
Set the Level switch to 1 as you only have one level being monitored.
Buzz out the float switch to figure out which wires you require and wire these to the min input.