Tough to be precise here with no good manuals to examine. But I can offer suggestions that are common for such hub systems.
ONE of the edge connectors on the right end of that Hub board is shown with a cable labelled "Fan LED SW". I expect this actually is a cable that comes from your case's front panel RESET switch (or perhaps a separate dedicated LED switch). Normally that button would be used manually to step through several pre-set lighting displays, and the system MAY re-set itself to a default first display pattern at each start-up. IF you had this in a system with NO other way to adjust the lights, this is the only way to make them change. BUT if you have been able to connect to this board a signal from your mobo's ARGB lighting header, then this board can be told to let that external signal take over. The way this is done on MANY systems is that you hold that front panel LED manual control button in for about 5 sec, and then it allows the external signal to take control. This process may have to be done at every start-up.
To accommodate that option, the board has a small 3-pin edge connector at the opposite (left) end of the board (upper left in your photo). I expect the cable from that goes to an ARGB header on your mobo. This is how your mobo's control signal can be sent to this board. NOTE that this cable MUST be plugged into a THREE-pin ARGB header on the mobo, and NOT to a 4-pin plain RGB header.
You mention using Polychrome Sync. That is a software utility supplied for use with ASRock mobos to control lighting via the mobo's ARGB header. So I assume that you have an ASRock mobo and are NOT trying to use that tool with a different mobo. Now recognize that such a system has no way of knowing where the signal sent out by its ARGB header goes, so the software tool never will tell you anything about a HUB. All it "knows" is whether or not its mobo header is working and a signal is being sent. So if that tool indicates it is working, it probably is. Then your dilemma is on the Hub board and its connections.
CHECK these items.
1. ALL things plugged into the Hub board - any loose connectors?
2. The other end of connecting cables where they get signals to use.
3. Power supply input to the board - on the left edge, wider connector lower down labelled 12 v - GND - 5V. Ensure it is connected and then check its other end. It should be plugged into a SATA or 4-pin Molex power output from the PSU.
Now try it out. Try the front panel LED or Reset button. If it does not seem to work, try this as first troubleshooting step.
DISconnect the 2-pin connector at top right ("Fan LED SW") and the one at top left with three wires (PC In). Reboot. What should happen is the fan lights and motors do come on in a default display but you cannot change that. If you still get nothing the board itself may be faulty. You can try one more step. Shut down and re-connect the 2-pin "Fan LED SW" connector to the upper right then reboot and see if things can work when you push the front panel LED or Reset button.
If things DO work, ensure the 3-wire cable is re-connected to the upper left board edge connector.