Operating the actuator from the power supply directly with a DMM on the 10A range in series with it will show you the steady state current. Loading it while operating will show loaded current. This should be far less than 10A.
Fuses are designed to 'blow' when the current exceeds their rating.
The actuator is presumably drawing more than 10A (probably just on startup) or there may be a short circuit on its output.
The actuator does not appear to have a current rating shown anywhere on the page you referenced. Operating current at full load at 12V would be expected to be a few amps. The startup current may be FAR higher.
Most likely solution: You could try using a 10A "slow blow" fuse, which is designed to carry a larger than rated current for a short period.
The fuse appears to be an automotive type possibly not available in slow-blow style.
If so, you could add an external 10A slow-blow fuse and use an eg 30A fuse internally.
YOU MUST have a fuse with no larger larger than 10A fusing current somewhere in the circuit. Using eg just a 30A fuse may damage the controller.
You could try using an automotive 12V lamp as a temporary load.
A 5W bulb will have a startup current of very roughly around 5A for a short period - then only about 0.5A.
A 20W bulb about 4x as much in each case.
A 50 W bulb about 10 x as much.
Seeing how the fuse reacts in each case will help to show if the controller is faulty.