Yeah I get the same thing and my screen is definitely flat. I have an astigmatism in one eye. And it works best late at night with 5cm x 5cm or smaller images. Especially images that have a slightly blurry background. I think it is partly psychological but it did not happen before I needed glasses to view the screen.
"Probably better depth perception due to clarity of images with your glasses on."
That is a terrible answer; the question clearly states that it occurs when viewing a computer screen or smart-phone screen. These are flat planes; there is no actual depth to them. (And no, the curved-screen displays on the horizon are not at consumer level yet, so it's safe to assume that the poster means common screens.)
I've noticed this effect just recently on my iMac screen and on my iPhone 5s, but only with particular images. "Trippy" is an apt way to put it; not something expect at all without special 3d glasses & projection. If I had to guess I'd say it has something to do with the curvature and/or material of the lenses and/or the result of special coatings that can be put on (anti-reflective, anti-scratch, etc.)
I recently got new glasses and noticed this too.
Seems especially evident on "terminal windows" where I am looking at lines of different colored text on a black background. Certain colors appear to be "closer" while others appear more distant. When next to eachother, creates a really trippy 3D effect. It freaked me out at first, but I am getting used to it and now think it looks kinda cool.
I am really curious though to hear a scientific explanation of this effect.
Probably better depth perception due to clarity of images with your glasses on.
JKCH MD