My personal experience is that in the beginning of Iodine supplementation when you're also full of things like fluoride and bromide, hypo and hyper symptoms take turn.
I think some reasons for this are:
The bromide that is clogging up your Iodine receptors in the thyroid make you hypothyroid.
When you take a salt push the bromide is flushed out (all or a bit) which makes you less hypothyroid or can even make you feel hyperthyroid for a while.
When you take lots of Iodine (I take way more then one gram for this reason) you flush out bromide which makes you less hypothyroid or can even make you feel hyperthyroid for a while.
Some things you eat might also influence this. Coconut oil for instance makes the thyroid work faster whereas unsaturated oils make the thyroid work slower. And then there's goitrogens etc...
Also there's the effect that fluoride has.
When you are really hyper (feel I mean, not TSH measured), does this stay longer than a week? Or does it pass within a few days? In my case it always passes within a few days. After that the hypo returns.
In my experience there's no such thing as too much iodine, except when your detox is just too brutal to bear. When that happens I lower my iodine and do salt pushes and drink a lot of water. Otherwise, I keep the iodine high (and do salt pushes and drink a lot of water :-) ).
This is what happens with me: when I lower my iodine my zits and other detox problems go away. Unfortunately I will get progressively tired (hypo) also. Pains start to return. My mind gets foggy. I get depressed and cold. Basically I get all the symptoms associated with bromide and hypothyroidism. When I return to my high levels after a few days, the first thing I notice is that my eyes start to be irritated and itch big time. My nose also joins in as does my throat. The mucous membranes just prick and itch like crazy (scratching, sneezing, etc). I can relieve this with salt pushes (which brings on the snot). What also happens though is that my energy level shoots up, my brain is clear and I return to a happy state.
My point is that while you're detoxing, you will experience all kinds of weird symptoms. Supporting the detox pathways helps. Making sure your body get all the nutrients it needs also lowers the gravity of the detox symptoms.
Concluding that you're hyper from a low TSH however is not productive in my opinion. The TSH can be either high or low for many reasons. http://www.violiendamast.nl/thyroid
Do you actually feel hyper? For longer than a week?
Maybe you can measure your morning temperature (before rising) to get a more objective picture.
When you're not feeling hyper, you're not hyper. The TSH is then low for some other reason. When your NIS's are rebuilt and you're taking ample iodine the TSH will get low because all things are progressing just as the body wants it, there's no need for the body to interfere by raising the TSH.