Today I heard in two (totally unrelated) videos the same unexpected pronunciation of the word 'assume' by native speakers. Googling came up with /əˈsjuːm/ both for English and American pronunciation (and that's also what I had expected. However, what I heard in those videos clearly was something like "a-shoom". Is that a specific dialect?
It is not so much incorrect as it is dialectal or personal (in the sense of how one pronounces things). I for one pronounce it as a-shyoom. I think it's a more British/Australian pronunciation.