well yes, the whole story is that there is also the “preview” pipeline which is displayed as the overview in the top left corner. it is always processed additionally to the center view, but at reduced resolution. this is sometimes needed as context for the full pipeline as well, in case it only processes a region (thread sync nightmare).
and yeah, large gaussian blurs or similar will require a lot of context. dt can also do that by requesting larger regions of interest from the input, i.e. pad the buffer up some. all of which is of course slow.
(the good news is that the abovementioned GPU code path is faster even when processing the image in full res all pixels all the time, so it will not have such surprises)