Microtubules are produced internally by the same sort of synthetic machinery that makes other cellular components. Many cell types have only a temporary demand for microtubules, and the cycling of materials through the pathways is controlled by internal and external signals. Upon depolymerization, they will move the two sets of chromosomes apart.
Microtubules are also involved in cellular movement as a whole.
Cilia and flagellae have a core of microtubules in a highly-conserved arrangement that causes them to move.