Consider the direction of current flow during an ESD event. If the discharge is from a negatively charged object, the lower diodes conduct, clamping the signal to one Vf drop below ground. If its from a positively charged object the top diodes conduct, clamping it to one Vf drop above Vdd. It can *NEVER* act to pull down the Vdd pin.
However it can cause the ESD protector's Vdd pin to rise till its Zener breaks down and passes enough current to handle the discharge. A sizeable low ESR and low ESL capacitance at the Vdd pin, e.g a pair of 1nF ceramics right next to the pin, and 100nF ceramic next to them to spread out the ESD discharge impulse thus reducing the peak Zener clamping voltage would be desirable. You'll have to determine if the rest of the system can tolerate Vdd surging to the Zener's clamping voltage, or whether you'll need to provide a dedicated clamping rail that can actually sink the surge current without rising excessively. If you can tolerate the signals rising to the Zener's clamping voltage (e.g. by resistors between the ESD protector and the I/O pins to limit the current in the I/O pins internal clamping diodes), it mayt be as simple as a resistor between the (decoupled) ESD protector Vdd pin and the main Vdd rail to limit the current at the peak clamping voltage to less than the minimum load on the Vdd rail. Resistors inline in the signals between the cable and the ESD protector can help considerably by limiting the peak surge current.
Running single-ended unbuffered logic level signals and logic Vcc supply over extended cabling is generally a poor idea, however you'll probably get away with it if the connectors aren't user accessible, the cable is screened and you can limit the slew rate to prevent excessive ground bounce. Good practice would be to use RS-422 transmitters and receivers, or RS485 transceivers at both ends, and run fused but unregulated power to the far end and regulate it there to power the remote logic. The differential signalling, and local Vdd regulation virtually eliminate the ground bounce issue, and many transceiver ICs are already well protected against ESD. Depending on the application, you may be able to tolerate half-duplex comms with TX and RX sharing the same pair in the cable, so may not need to increase the number of wires in the cable.