The t inside Animate[Plot3D[ww2, {x, 0, 1}, {y, 0, 1}], {t, 0, 0.6}] is "localized," which means it is different than the t that shows up when ww2 is evaluated. Animate[] will replace all literally-occurring instances of the symbol t with the localized variable; however, Plot3D[ww2, {x, 0, 1}, {y, 0, 1}] contains no t. Yes, as I implied, the value of ww2 contains a t, but ww2 unevaluated is just the symbol ww2: no t. So when Animate[] sets the value of the local t, it does not affect the value of ww2.

Animate[] does this so that the value of t outside the animation is not changed. This is important because when Animate[] changes the value t inside the animation, the change triggers a Dynamic[]-related update that redraws the plot. If you change the value of (global) t outside the animation, it won't affect the animation because it's a different t; and likewise, the changes Animate[] makes do not affect any calculations while the animation is running.

To get it to work you can use @Gianluca's With[] code. Or you could do this:

ww2[t_] = ww[x, y, t] /. ParameterValues;
Animate[Plot3D[ww2[t], {x, 0, 1}, {y, 0, 1}, 
  PlotRange -> {-0.0002, 0.0002}], {t, 0, 0.6}, 
 AnimationRunning -> False]

Or this:

Animate[Plot3D[ww[x, y, t] /. ParameterValues, {x, 0, 1}, {y, 0, 1}, 
  PlotRange -> {-0.0002, 0.0002}], {t, 0, 0.6}, 
 AnimationRunning -> False]

There's also an option, LocalizeVariables -> False, you could use, but many avoid that for the reasons given in my second paragraph: It makes the animation interact (unpredictably) with any calculation that is using the variable t at the same time.