From the instruction manual, this looks like 2-stage boost controller.
The ball&spring piece (T-piece) set the initial boost and the in-cabin bleed valve increases boost level.
If this is so, the exhaust hose doesn't have to connect to anything.
Try tighten the bleeder piece and see if your boost still creeps up.
If it still creeps up, you are having a problem with the ball & spring piece.
The spring is either too stiff or the ball get stuck and doesn't let any air passes through.
Using air compressor, try applying air pressure to that input port.
It should start opening and lets air through at 7 psi or whatever initial setting of that boost controller.