A photo or two would be VERY helpful for us to help answer your question.
The tuyeres should be as close to an airtight fit as possible, you want the combustion air to be forced out of the air slots in the tuyere, not leaking out at the base of the tuyere.
It probably is just a bit of filing or minor grinding with a Dremel or small grinder to clean up the 'hooks' you describe so that they properly hook into the air chamber under the tuyere.
Photos would definitely help !!