Electrical – Splitting a three phase contactor

Do you have the DC supplies and Arduino grounds connected together? If not then any PWM from the Arduino will not work.
Most small plug type DC supplies are floating, so their grounds will not be connected to USB ground (of course the USB ground may be floating if e.g. on laptop battery)

As Russell mentioned a diagram of your connections would be useful.

Thanks for the diagrams:

Your problem is as stated above, you need to connect the grounds together. Otherwise, the Arduino PWM signal has no return path (remember a voltage is always relative to something) to Arduino ground since the grounds are not connected.
It's okay to connect all the grounds together (arduino and DC supplies)
The only time is isn't is in the very rare case where you might have a supply "ground" that is above earth ground relative to supply grounds (e.g. a 20 V supply with V+ at 50V and V- at 30V relative to earth/AC ground could not be connected to a 20V supply with V+ at 20V and V- at 0V)
If in doubt you can test for any voltage between the grounds with a multimeter (e.g. one probe to one ground, one to the other ground) but since most DC supplies are floating (not referenced to earth ground) then essentially the outputs are just like batteries.

Hope I haven't confused things here :-) Connect them together and let us know how it goes. Here's an altered version of your diagram (note extra black ground lines):

From photo it is seen that each relay has input and output connection, therfore a simple rearangemnt of wires can drive a heater in a star connection with neutral in the middle. This is a part of yours PCB schematics and proper connection to 3ph network 230/400V:

^{simulate this circuit – Schematic created using CircuitLab}

EDIT:
ad 1st) Use 5 wires of 2.5mm^2 cross section. Don't mix the colours, use standard CE colours: black for phase 3 wires, blue for neutral (or you might consider buying a cable 5x2.5mm^2 in this case you get black, brown, grey for phase, blue, yellow/green), yellow/green for earth. Install an overcurrent protection device 3x16A in your main cabinet. Now what you need is L1, L2, L3, N, PE wires (five of them).
ad 2nd) Phase sequence is not important, you can mix them.
ad 3rd) See my schematics: If you measure from N to any element you get resistance of one element R, if you measure between two of them you get a series resistance of two of them 2R. You got 28 and 50ohm which is close to R and 2R.
ad 4th) The free connections are one end from each element (red wires on your heater), while the second ends are connected together in star - the jumper you see that connect three heater ends, where the neutral is attached (black wire).