Driving a ThorLabs piezo controller with TTL external input
The data page that you linked says specifically that the external trigger inputs are meant to operate at 5V. There is a good possibility that your inability to get the performance that you desire is related to your trying to trigger the input with only a 3.3V signal. 

I suggest that you try prototyping a simple 3.3V to 5V logic level translator that uses an active push-pull drive output to the controller to see if that improves the performance. If you can get your hands on a 74HCT125A chip it offers an extremely convenient single chip way to convert a 3.3V signal to a 5V drive signal. Power the VCC of the chip from 5V and ground the OE pins.