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?
As described in this ELU answer, the pronunciation of assume in most British and Australian accents is /əˈsjuːm/ with the /s/ followed by a yod ('y' as in you). There's a tendency to merge an /s/ with the following /j/ ('y') to /ʃ/ ('sh' sound), so most people merge them to /ʃ/: [əˈʃuːm] (a-shoom). [Assimilation]
By contrast, in most North American accents, the cluster /sj-/ has been simplified to /s-/, so they might pronounce it [əˈsuːm] (a-soom).
Another example is bless you pronounced bleshoo in fast speech.
And according to another answer, [əˈsjuːm] is the normal pronunciation of 'assume' in British English but it's possible though that some people might pronounce it [əˈʃuːm] in rapid speech and it isn't strange at all.