Is this behavior-as-intended (i.e. the feature is intended for marking duplicates within one site, and cross-posted duplicates should be reported some other way)
Yes. In a general sense, it's actually fine to have questions "duplicated" across sites - provided they're addressing different audiences. Of course, if a question is off-topic, or if a user is simply re-posting the exact same question on multiple sites (cross-posting), it should be migrated to the site where it's most on-topic and dealt with there.
###See also: What to do with cross-site duplicates?