While playing, especially at the faster difficulties, it looks like that moving the cursor in the opposite sense of the rotation of the hexagon makes you go slightly faster. Is this true or it's just an optical illusion?
No. Your cursor moves at a constant speed relative to the constantly spinning board. This means that, if all the spinning and perspective shifts were removed, your cursor would always move at the same speed, regardless of which way you're going.
The cursor certainly moves faster or slower relative to the screen, based on the way the board is spinning, but it always moves at the same rate relative to the board itself.