Is there a recommended power-up sequence?

Yes. The relevant product data sheet provides a recommended start-up sequence to refer to before powering up the device.

Generally, it is good practice to connect the ground first, then power the V_DD pin and the V_SS pin second. The order of the voltages at Terminal A, Terminal B, and Terminal W (V_A, V_B, and V_W, respectively) is not important, but power these last.

There are ESD protection diodes between the V_DD pin and Terminal A, Terminal B, and Terminal W. For example, the cathode of one of the diodes connects to the V_DD pin and the anode connects to Terminal A. As a result, any voltage occurring at Terminal A before the V_DD pin forward biases the diode and powers the V_DD pin.

For some of the digital potentiometers, power the digital signals after the V_DD pin. This power sequence is documented in the relevant product data sheet.