If you open lots of Tabs in the TabPane, and you scroll up with your mouse wheel you will go to the right, if you scroll down, you will go to the left.

But, IMHO, I've checked how Firefox and Netbeans are reacting and it's the opposite. I did not find any documenttion on a specific behavior but apparently it's the common setting on Window:
wheel down = scroll right
wheel up = scroll left

In order to resolve that issue, you should only modify the TabPaneSkin in that way :
"addEventHandler(ScrollEvent.SCROLL, (ScrollEvent e) -> {
                Side side = getSkinnable().getSide();
                side = side == null ? Side.TOP : side;
                switch (side) {
                    default:
                    case TOP:
                    case BOTTOM:
                        setScrollOffset(scrollOffset + e.getDeltaY());
                        break;
                    case LEFT:
                    case RIGHT:
                        setScrollOffset(scrollOffset - e.getDeltaY());
                        break;
                }

            });'"