It would be reacting through electrophilic aromatic substitution. In base, phenols are pretty strong nucleophiles. Even with no catalyst phenol reacts with most/all halogens. I don't think traditional CHI3 (Iodoform) product would be forming. But the iodine you add would get used up, changing the color/appearance of the solution.
In the product, hydrogens on the ring ortho/para to the hydroxyl groups would be replaced with iodines.