Start the control circuit first, followed by the other circuitry. Then, apply the control signals to place internal logic in a steady state and then apply other signals. The order is similar for bidirectional dual-power level shifters (buffer type) and unidirectional dual-power level shifters (buffer type).
Apply power supply and other signals in the following order. (Fig. 1)
#1. VCCA (power supply for circuit blocks with control circuits)
#2. VCCB (VCCA and VCCB may be powered up simultaneously.)
#3. Control signals (/OE, DIR)
#4. Input signals (A1 or B1)
The same order applies to the level shifter (bus switch type). (Fig. 2)
The following documents also contain related information.