Colchicine is an alkaloid and a secondary metabolite of the plant- a crocus, primarily functioning to protect the plant (like, from consumption by herbivores).
WHY COLCHICINE DOES NOT AFFECT THE PLANT:
It is transported far away from its site of production to the tissue storing it so does not come in contact with normal metabolically active plant cell machinery.
In the storage tissues colchicine is compatmentalised in vacuoles specific for colchicine storage.
The vacuoles are bounded by tonoplast which contains special proteins that facilitate active uptake of colchicine from the cytoplasm into the vacuole protoplast but do not conduct the movement of colchicine from the vacuole to the cytoplasm.
The scientific studies are detailed here.