Unbalanced forces act on an object when there is a net force, meaning that the forces acting on the object do not cancel each other out.
In the scenarios you've provided, the situation where unbalanced forces are acting on the tire is: "Two people stand on the same side of a large tire. One person pushes the tire and the other pulls the tire with equal force."
In this case, the forces are not acting in the same direction, leading to a net force on the tire, which would cause it to move.