that potentiometer, labelled T - the one that is turned most clockwise - is probably the timer adjustment in question. If you alter this, does it alter the timeout period? This will probably be in series with another resistor. Turning it far clockwise takes the resistance to its minimum and the extra resistor is the residual 3 minutes. therefore you want to lower this fixed resistor. I would lower it, but not reduce it to zero (I dont like zero ohms in any circuit).
This is just a guess, but probably how it works. I have an en suite timer with the same problem. The above worked for me