This sounds like a common problem with the winding ends going to the wrong phases.
If the starter performs correctly in star, I would say that the motor is fine.
I would recommend that you use a multimeter to identify and mark both ends of each winding group. Assume that the ends going to the star or wye contactor are the finishes and the other ends are the starts.
Positively label each with winding number and start or finish.
Number the incoming phases, 1,2 3 and ensure that the order across the input of the main contactor and the delta contactor are the same. I usually check by measuring L1 on K1 (Main contactor) to L1 on K2 (Delta contactor) then L2 on K1 to L2 on K2 and L3 on K1 to L3 on K2.
Next connect the finish of winding 2 (start connected to phase 2 of the main contactor) to the output T1 (phase 1) of the delta contactor. Connect the finish of winding 3 to T2 of the delta contactor and the finish of winding 1 to T3 of the delta contactor.
To prove that you have it right, isolate the coil of the delta contactor and initiate a start. When the main contactor is closed, and the delta contactor is open, measure input to output on each phase of the delta contactor. You should get phase to phase voltage (i.e. 480 V) on each phase. If you do not get equal voltages across each phase of the contactor, you have a wiring problem.
Best regards,
Mark.
Mark Empson
L M Photonics Ltd