You'll need two insulated track sections; one before the signal, the signal bridge itself in the middle, and another insulated track section after the signal.
South ===== I ===== North
The section south of the signal controls the southbound signal head and the section north of the signal controls the northbound signal head.
A northbound train sees only a green light but as he enters the insulated track section (the first block) before the signal, the opposing light turns red. As he passes under the signal bridge and onto the next block, the northbound signal will turn red as well (both directions will show red). The southbound signal will return to green as the end of the train clears the first block. And the northbound signal will return to green when the end of the train clears the second block. That's very prototypical operation.
Now you want to use your 4 channel relay board instead of the relays shown in the circuit diagram that you posted. I've got a similar relay board that operates on 5 volts with optoisolation. So mine is different than what you've got. What are the jumpers for (I see one for each channel) ? Does yours provide optoisolation (opto-couplers) ?
When it comes to the AC negative coming off the insulated rail, I get kinda confused. As long as your transformers are in phase (the U terminals tied together and the plugs all turned in the right direction), you can power the relays from an independent power source. For you, that would be your 12 volt wall wart which you will have to get in phase with your other transformer(s). But the wall wart puts out DC and the trains run on AC. This is where I get confused. Maybe Stan can clear this up for both of us.
Otherwise, I think you're on the right track. The circuit minus the second track looks fine.
