I would expect that board (dx.com) is active high as there are no optocouplers, only a single transistor (or fet) per coil.
I would be very cautious with using the typical Chinese relay boards on a commercial product, personally, I would never do that. The majority of the boards out there do not meet basic US safety standards for minimum creepage and clearance distances to prevent flash-over on both the lv and hv sides of the relays. There are a few boards with good quality relays and correct board layout/routing but they are the exceptions, not the rule.
Feel free to prototype with them but put them into field, especially into a big citiy where inspectors look for a UL label on everything, never.