You need an ANALOG voltage (0-5V) to drive the pump controller.
The PWM outputs are DIGITAL (Pulse Width Modulated) - which can be put through a filter to generate a low-current pseudo analog voltage.
You will be better off using a separate Digital-to-Analog converter chip/module to generate a stable voltage signal based on the value you set from the Arduino.
Edit: Corrected typo ADC/DAC