When using multimeter to measure VIN-GND or VCC-GND voltage, make sure you are measuring in DC, not AC. On a standard multimeter, DC voltage is marked as a V with a flat line above it; AC voltage is marked as a V with a curvy line above it. If VIN-GND is 5V, that’s correct. You said VCC-GND is 4V and 7V by your two meters, that seems to suggest a problem. VCC-GND should be 3.3V.
Going back to the instructions:
did you check the resistance between VIN-GND and VCC-GND? Are they within acceptable range?
Also, to isolate the problem, I suggest that you power the controller with a USB cable first, and check voltage, then move on to use sprinkler transformer. This can help diagnose whether the problem is in the 5V to 3.3V conversion and beyond, or it’s in 24VAC to 5VDC conversion.