I’ve plugged the HHC into the ‘inc/dec’ input of the Trigger i/o but when I step on the pedal, pulling the chain down will not send a MIDI message, rather it will scroll through the selected parameter of the Trigger i/o.

From looking at the Trigger I/O manual, I think you want to plug into input #9. The one that is labeled Hi-Hat.

The ‘Inc/Dec’ input is where you can hook up a dual footswitch button to remotely increment and decrement values from your dualfootswitch.