Explanation request of a circuit involving contactors, transformer and a 3-phase motor
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. A possible reinterpretation of the OP's schematic.


In this configuration the transformer primaries and secondaries are shown in star (wye) configuration. The transformers step down the voltage.
On power-up the motor is fed with the reduced voltage from the transformer.
After a time delay all contacts switch simultaneously from reduced voltage to high voltage (switches in position shown).




Since you are quite sure that the "transformer" remains connected to the motor when the contacts are closed I suspect that it may be a set of series inductors or "chokes" to reduce the starting current.







simulate this circuit

Figure 2. Soft start using inductors.

I've never seen such a system and the sequential closing of the contacts is strange as it will imbalance the three phases.