Well, the main point is that BEFORE the quake the water air interface represents a geopotential surface... that is other than minor effects of winds the water level is defined as a surface along which the potential energy is minimized. In a rotationless and wind free world this level would be the equilibrium condition consistent with sea floor topography.

Now in a large quake there is a permanent alteration of the sea bed in a bathymetric sense.... the water lying above suddenly and catastrophically moves to find the NEW geopotential surface. This necessitates movement of water... any excitation will cause a wave or waves to form and all waves have troughs and crests...

The devil is in the details... exactly how did the sea floor level change and what the configuration of the shallow sea near the beaches....

You might go here and see if you can find some simulations:
click-here
video-play

Its a geometric issue associated with the very nature of a deep water gravity wave.

First from the derivation you realize that the trough and the crest are just parts of the same deformation of the surface.

Go hereto see derivation based on the PDE
click-here

Another analysis is found at
click-here

Basically the trough and the crest are part of the same beast...cant have one without the other...the trough leads because that is what builds the crest.

This is a water slosh that encompasses the full depth of the water. Now, on the figure, the arrow shows where we suddenly pull down on the crust. This is our big subduction earthquake. The water sloshes into the hole, and this starts to propagate over to Padang and Africa (negative slosh). It doesn't take long for the water to slam together, and send out a positive slosh. These slosh pulses involve the whole depth of the ocean, and travel quite slowly, as one would expect.

In one way, the people may be luckier with a big subduction earthquake, because the pull-down causes a leading negative slosh. Thus, when confronted with the ocean disappearing, it behooves one to run like hell to higher ground! Apparently, this might be too late for Padang; they have to start running as soon as they feel the shaking, because the run-up could be kilometers!