How does a TVS absorb voltage?
In an ideal circuit with a perfect voltage source and no parasitic resistance, you would be right -- even if the transient voltage suppressor (TVS) conducts 100 A of current the damaging voltage would still be present on other components.

It's the parasitic effects that let the TVS work.  There is resistance and inductance in the traces, vias, and pins, and there is capacitance at various points (bypass capacitors placed on the PCB, internal bypass capacitance on an IC, parasitic capacitance).  All of this means that when the voltage is briefly too high at the TVS, it will not immediately be so high at the downstream circuits.  

Of course, if you force an overvoltage condition for long enough, it will still damage the circuits, but that would no longer qualify as a "transient voltage" to be suppressed.