Sling Mapping will work even if Rewriting is disabled in Transformer
which is why ur short url is working when u hit in browser, but updating
content full urls to short urls will not work in html source. For other
project its working, reason might be they have a custom rewriter written
in other project which implements TransformerFactory. So you need to
update setting of other custom rewriter for new project.
You can find the component used for this under
comment. You can overlay or extend based on your requirement. Since this
is OOTB dam feature, better not tamper it unless strong usecase.