I have thought of a conjecture which could explain why some people experience detox symptoms so far into supplementation.
3.mg of Iodine isn't very much if you're dealing with parasitical infections which have progressed over years, for example.
If you're dealing with biofilms, then higher doses are needed to see faster eradication. When the Iodine finally opens up the biofilm wall which can take months with that dose, only at that point will the immune system really attack the pathogens which subsequently get released.
Now, as I said, this is pure conjecture so just take what I said with a grain of salt. For me, this explanations seems logical enough.