The most general compositing hosts allow images to be of any size at any location on our image plane. They also plumb the output of effects into other effects, to create effect trees. When evaluating this tree of effects, a general host will want to render the minimum number of pixels it needs to fill in the final desired image. Typically the top level of this compositing tree is being rendered at a certain project size, for example PAL SD, 2K film and so on. This is where the RoD/RoI calls come in handy.
The host asks the top effect how much picture information it can produce, which in turn asks effects below it their RoDs and so on until leaf effects are reached, which report back up the tree until the top effect calculates its RoD and reports back to the host. The host typically clips that RoD to its project size.
Having determined in this way the window it wants rendered at the top effect, the host asks the top node the regions of interest on each of it's inputs. This again propagates down the effect tree until leaf nodes are encountered. These regions of interest are cached at effect for later use.
At this point the host can start rendering, from the bottom of the tree upwards, by asking each effect to fill in the region of interest that was previously specified in the RoI walk. These regions are then passed to the next level up to render and so on.
Another complication is tiling. If a host tiles, it will need to walk the tree and perform the RoI calculation for each tile that it renders.
The details may differ on specific hosts, but this is more or less the most generic way compositing hosts currently work.