The TPS621351 is capable of starting into a pre-biased output. The device only starts switching when the internal Soft-Start ramp is equal or higher than the feedback voltage. If the voltage at the feedback pin is biased to a higher voltage than the nominal value, the TPS621351 does not start switching unless the voltage at the feedback pin drops to the target.

This functionality actually also applies to TPS62135 but the discharge function in TPS62135 keeps the voltage close to 0 V, so starting into a pre-biased output does not apply.