In a 120/240 volt transformer, there is no center of the winding. There are two 120 windings each giving 120 volts from one beginning to the end of the winding.
Then one winding from the last of said two that 240 windings giving 240 volts.
If its one thing i know, its how transformers the electric company uses, as i did linework for 32 years.
I am seeing no out of phase, just the difference in adding the other 120 windings to get said 240 volts, thats how it works.
All 3 windings of the transformer, primary one of the 120 and the other 120 winding are going up and down, alternating at the same rate and time, thats how it works. The neutral carries the unbalance that is constantly changing.