The I/O terminals that input signals do not need pull-up resistors, and the I/O terminals that output signals need to be pulled up to the power supply on the output side.
A dual power bus switch has the feature that the switch is turned off when the input signal of terminal A (or terminal B) exceeds the reference voltage based on VCCA.
This feature is used for voltage level shifting (level shifting).
Therefore, a pull-up resistor is not required on the input side of the signal, and it is necessary to pull up on the output side to the power supply on the output side.
When using in both directions (Fig. 1), a pull-up resistor (Rpullup-A, Rpullup-B) is required at both pins because both A and B sides may be output.
When using the input side and output side in one direction (Fig. 2), a pull-up resistor is not required at the input terminal (A side), but the output terminal (B side) must be pulled up (Rpullup-B) to the power VCCB at the output side.
When using in one direction in the reverse direction, a pull-up resistor is not required for the input pin (B side), but it is required to pull up (Rpullup-A) the output pin (A side) to the power VCCA of the output side.
The following documents also contain related information.