Your mesh is still in quads, but it is just being displayed in tri's, (notice that the white lines arent for the tri's, but only the edited quads)
There is an option to change in the viewport driver settings to turn off that kind of display (this will make it look like Wiro's tut), but this is the true way to look at it, as this kind of triangulation is really happening, and the other way just hides it. I prefer the other way though

makes me feel cleaner like the cleaning lady.