Hi, thank you for your interest, let's hope we can tackle this issue quickly!
We have developed and tested controller input using XBox controllers - they should work fine, although we are aware of some UI issues.
We haven't tested with Dualshock controllers which I'm trying to get hold of right now - so we could test and implement them properly. There hasn't been a request for that and we were focusing on other parts of the game, apologies for that.
In the meantime, could you try entering rebind keys menu through Options -> Gameplay Settings -> Clicking on any of the keybinds and trying to use DS controller to bind a key? I'd like to know if our defaults are wrong or the controller is not detected entirely.
Also could you try using Sipho version found in Steam's beta branch called [staging] which has newer version of the game built with a newer version of the engine - it might have DS controller support added there.

Please let me know how it goes, making this game available for everyone to play is our priority.

Hi again, I've just tested input with Dualshock 4 - it works when connected through wired connection, but fails to register Left-Stick Down - due to a workaround to an engine bug which is now fixed. Upcoming version 0.7.8 will have this fixed, we hope to have it in few days. Thank you for reporting this