Have you checked that the leads are connected to the right terminals? And pushed right in! (half way in can reverse the signal)
Your symptoms suggest something being reversed perhaps? (A noise when releasing the pedal)
Ps. 'pedal held down' and hihat hit with a stick should be a metallic 'tapping' sound.
'Pedal released' and hihat hit with a stick should be a noisy splashy cymbal sound.
I think my description was not really good, I do have a normal behaviour of the pedal if I keep it pressed or released, with normal sounds for the corresponding closed or opened hi hat positions.
What I don't have consistently is the chick and splash sounds, I can make them maybe 60 or 70% of the time only and when I do them the pedal makes a loud mechanical noise when released (but this mechanical noise when released is exaclty the same on the above videos so I'm assuming this part of my issue is "normal").
In the meantime I've contacted Alesis and they asked me to send them a video record of the inconsistent chick and splash sounds, so now I'm trying to figure how I'm going to do that considering I don't have speakers connected to the drum kit.
In the end if they cannot solve the issue I think I'm just going to live with it for now. It doesn't seem to be really an issue for a complete beginner like me and the day I become more proficient I can still move to a better kit or upgrade this one with a real hi hat stand
I also ordered a Trigerra kick pedal Trigger as my neighbour was complaining about the noise from the bass pedal