In general, The dual-power bus switch has no restrictions on the order in which the power is turned on and off. The device will not be damaged even if either power supply is turned on first. However, there may be restrictions on the power-on order, so please check the datasheet of each device for details.
The operation at power-up are described using TC7WPB9306FK as an example. (refer Fig. 1)
When VCCA is turned on and VCCB is turned on later, the switch does not turn on until about 1.5 V because the voltage enough to turn the switch on is not applied to the gate of the switch.
Also, if VCCB is on and VCCA is 0 V, the gate level converter will not start, so the switch will not turn on.
However, to use this device as a voltage level conversion IC (level shifter), please use at the condition (VCCA < VCCB).
The following documents also contain related information.