Today I have reported two bugs about tab scroll with mouse wheel:
but the list of affected programs is bit broader and we need to decide how should we follow MATE HIG:
If present on the mouse, the scrollwheel should scroll the window or control under the pointer, if it supports scrolling. Initiating scrolling in this way should not move keyboard focus to the window or control being scrolled.
If it supports both horizontal and vertical scrolling, perhaps suggest unmodified scrollwheel should scroll vertically, and <Shift>+scrollwheel should scroll horizontally.
Patching every app with GTK_NOTEBOOK may be difficult and ineffective.
And other problem is that non-MATE applications may not have these patches...