it would appear, that on a structural level, an ear is not damaged by the use of headphones, noise cancelling or otherwise, unless used at abnormally high volumes (e.g., > 80db for extended periods)
that being, said, there is little doubt that tinnitus can be caused by (especially noise cancelling) headphones, if you go see your ENT or audiologist, there is not likely to be anything (structurally) found that explains your symptoms, and you probably will pass a hearing test with "flying colors," assuming you had no prior / pre-existing issues
think of it like this, the ear and its many fine parts are the receiver, but the brain circuitry is the amplifier, so if you "shut down" or limit the receivers capability, then your brain will try to amplify any little signal it gets, and this will get worse with time, hence causing tinnitus...
this is why tinnitus (most of the time) is associated with hearing loss, the hearing loss (structural damage) comes first, and then your brain tries to amplify what signals it still gets from the damaged receiver (your ear), even if the receiver is completely removed and the person becomes deaf, there still may be sounds / tinnitus perceived in your brain, just like a person who has a leg amputated, may wake up and experience pain in the missing limb, a.k.a., phantom pain...
a noise cancelling headphone, is artificially creating "hearing loss," and your brain (amplifier) will not know the difference between this and real structural damage... the loss of signal is the same...
most of the time, this will go away, when the headphone is not used, but it may take a long time, and if the headphone is used extensively, it is, at least theoretically possible, your amplifier (brain) will be "rewired" for good and the tinnitus will never completely go away...
in short, if you are experiencing tinnitus following noise cancelling headphone use, 1) go see an ENT and audiologist to verify there are no structural issues with your receiver, i.e., your ear and its circuitry, 2) if number one does not find a cause and there is no hearing loss, then it is STRONGLY advisable you STOP using your noise cancelling headphone for good, as, and at this time, there is ZERO data nor any good scientific evidence, for how long tinnitus will last and / or whether (in some cases) it can progress to permanent rewiring of brain circuitry, i.e., you will essentially induce a phantom hearing that will not go away...
if you already are one of the people (nobody knows how many are affected) whom is suffering from long term tinnitus and has no structural damage to the ear, then, Cognitive Behavioral Therapy, likely is your best option, also you can try other things such as "white noise" distraction, mindfulness and meditation, there is no pill, vitamin or other supplement that will help