What it looks like to me is that someone has hooked the 2 transformers together and knew enough to get them in the same phase. This works however if a transformer is replaced or any wires are changed then you have the penitential to create 48 volts which will cause damage to components attached to the circuit.
The best way to deal with this is to use more conventional wiring methods or make sure that 24 volts is all that is present.
Phasing is simply accomplished by trying different wire combinations from the transformers with a meter until the output is 24 volts. What is happening is that the 2 transformers are sharing the same wire which works until something goes wrong and then it is a bit more complicated to repair.
The short answer to your question is if you take a meter and the potential between the r terminals at the thermostat and the c wire hooked to the transformer in the air handler reads 24 volts it should be fine, however it is risky to do this.
The best way to deal with this is to use more conventional wiring methods or make sure that 24 volts is all that is present.
Phasing is simply accomplished by trying different wire combinations from the transformers with a meter until the output is 24 volts. What is happening is that the 2 transformers are sharing the same wire which works until something goes wrong and then it is a bit more complicated to repair.
The short answer to your question is if you take a meter and the potential between the r terminals at the thermostat and the c wire hooked to the transformer in the air handler reads 24 volts it should be fine, however it is risky to do this.