You're quoting me out of context there.
When I said "depending on where is best to mount it/which side of the wall [that youre going to saw through] has the best airtightness" (the rest of the sentence you snipped) I meant:
If there's some gaping hole in the extension, e.g. the eaves of the roof are unfinished/there's no plasterboard/etc, then it doesn't make much sense to put your extract fan in the extension and use negative pressure to suck the dust away from entering the rest of the house, so you'd mount it in a window of the house, then apply positive pressure to the house to blow the dust into the extension..
Conversely, if the house is a draughty old victorian semi and the extension is brand new, well built and sealed really well then you're best off mounting the fan in the extension and running negative pressure...
Ergo, pick whichever side of the to-be-cut wall is the most airtight, and apply the relevant positive/negative pressure to that side for best results