some of it went into the air. to test, mix some starch in water and spray it on a washable surface in the room. it will stain dark blue, i bet. that idoine will corrode metal hinges, knobs, the motor on the exhaust fan, etc.
povidone is Iodine trapped in a polymer and is released slowly. that is why you still had color.
for us yankees, Lugols is too precious to put in a bath. i did it while i could but i am not likely to do it again without a change in Iodine status.