quastion

You start a 3 phase motor in "star mode" to reduce the start up current. In star connection, the voltage on the winding is less than in delta mode. Once the motor has started turning, you can then switch up to a higher voltage by rewiring as delta mode.

There is always a very short delay between the turning off of the star mode voltage and the turning on of the delta mode voltage. If you are using relays, just ensuring the correct order is enough of a delay.

Arguably, you could do it in a shorter timespan, as in ultrafast transfer switching, but you would need to repect the phasing differences, current extinguishing periods and order of phase reconnection. This would increase complexity and cost for possibly little functional advantage.

RL

The rotor currect will take a little time to die away but you can take advantage of the slip frequency to prevent the engaging delta from making a large spike. This means that the phase step between star and delta would be in the lagging direction.