The mesh is still adaptive, but with less refinement. (Note the small triangles in the corners.)
Mesh refinement is based on the angles between polygons, and is computed using the natural coordinate system, without accounting for the rescaling that comes from
Plot3D setting the
BoxRatios option. If we set
BoxRatios->Automatic, then we can see that your second plot is stretched out to the point that it is "flat" enough to not trigger very much refinement (just the corners and a bit near (4,-2) for the tallest peak.)
Plot3D[f[x, y], {x, 0, 1}, {y, 0, 1},
BoxRatios -> Automatic, Mesh -> All]
Plot3D[f[x/8 + 1/2, y/8 + 1/2], {x, -4, 4}, {y, -4, 4},
BoxRatios -> Automatic, Mesh -> All]
You can see how the refinement changes with scale with the following
Manipulate:
Manipulate[
Plot3D[f[x/(2 n) + 1/2, y/(2 n) + 1/2], {x, -n, n}, {y, -n, n},
PerformanceGoal -> "Quality", Mesh -> All],
{n, 0.5, 5}]
