Sonic Scream: Siryn can use Pulse Wave. When she uses Pulse Wave and has no action tokens, each character hit also receives an action token.

Since Pulse Wave ignores powers and abilities, if Siryn hits a character that already has an action token and Willpower, will the Willpower be ignored and the second token placed by this power cause pushing damage?
Possibly. Pulse Wave ignores powes, abilities, feats, etc. until the action resolves. Pushing damage is dealt when the action resolves.

So both effects (the end of PW ignoring the powers and such and the application of push damage) occur at the same time and the active player gets to then choose the order the effects happen. Since the active player is most likely Siryn's controller, chances are that player will choose to deal pushing damage prior to the return of the ignored effects (so the push damage would occur). If for some reason that player did not wish to deal extra damage, though, that player could choose to let the ignored effects resume first.

Updated Q&A to reflect new timing on pushing damage.