The Phantom and the Hunchback of Notre Dame are odd cases in that, yes, they're the original Universal Monsters, dating back to the silent era, but they never interacted with the other Monsters in the later films.
I'm not sure either of them really qualifies as a "monster," though. They're just people with severe physical deformities. They were both ostracized and treated like monsters because of the people's intolerance of their appearance, much like Frankenstein's Monster, but they were both just ordinary humans otherwise. There have been other physically deformed humans in Universal films who were not considered monsters, like Fritz and Ygor. All the full-fledged Universal Monsters are either cursed supernatural entities (vampire, undead mummy, lycanthrope) or scientific anomalies (reanimated cadaverous construct, invisible person, evolutionary missing link).
It's only a problem if you let it be one. Aren't the literary Dracula and Frankenstein set about a Century apart?
At least. The events of Frankenstein (the novel) are dated "17--," while Dracula is set in 1890. The movie version of Frankenstein is apparently set sometime around the turn of the 20th century; I'm not sure when the Dracula movie is set. However, the advantage of having immortal characters is that their relative chronology ceases to be much of an issue.