I would suggest the solution is dead simple.

Turn the water off and remove the cistern.
Lift the cistern off and you'll see a plastic pressure valve (bomb) on the end of the siphon with a thin tube (15mm ish)
On the end of the tube is a half moon washer with the flat side looking down, if the washer is ok, position it on the tip of the tube, and reassemble, making sure the tube goes in the small hole.
Clean inside the pan where the tube goes to make sure you get a good seal first.
The reason the water is rising is because the washer isn't sealing, and letting air into the second chamber.