(Note: this is in rough form why I flesh out the details with @ssastry :) - @ssastry feel free to flesh out the description with as much information as possible)
For transclusions (parser functions and templates), Parsoid queries the expandtemplates API endpoint to fetch the expanded wikitext and parses that.
See the output of http://pagebanner.wmflabs.org/w/api.php?action=expandtemplates text={{PAGEBANNER:Toledo_banner_Puerta_de_Alfonso_VI.jpg}}
Compare against the output of http://pagebanner.wmflabs.org/w/api.php?action=expandtemplates text={{uc:Toledo_banner_Puerta_de_Alfonso_VI.jpg}}
The expandtemplates API endpoint should be able to return the wikitext corresponding to the execution of a transclusion / parser function.
Similarly the parse API endpoint should be able to return the parsed HTML corresponding to the wikitext.
But, see http://pagebanner.wmflabs.org/w/api.php?action=parse&text={{PAGEBANNER:Toledo_banner_Puerta_de_Alfonso_VI.jpg}}
Again, compare with http://pagebanner.wmflabs.org/w/api.php?action=parse&text={{uc:Toledo_banner_Puerta_de_Alfonso_VI.jpg}}