Croatia was divided--Dalmatia belonged to the Austrian half but much of inland Croatia was part of the Hungarian half of the empire. The Military Frontier had only recently been added to "civil" Croatia (1881 or something like that).
Modern ideas of national identity seem to have spread to that area only in the 19th century. Before that most people probably thought of their identity in religious terms (Orthodox, Catholic, Muslim, Jewish) rather than ethnic terms. Later, both the Serbs and the Croats tried to claim that the Bosnian Muslims belonged to their group.
Among immigrants to the US (who mostly came before 1921), a lot of them still answered "Austria" for the census question for place of birth rather than Yugoslavia even after Yugoslavia had come into existence.
The history of the Balkans from say 1850 to 1914 is really interesting. All these different groups were trying to gain the allegiance of what were often called “emerging nationalities.”
In actual fact these nationalities were in the process of being invented. Different groups claimed “historical right” to particular areas because they’d controlled a big chunk of land 600 or 800 years before for a decade or two. My personal favorite is the Serbs claiming they “owned” most of the Balkans because Stephen Dushan had an empire for 25 years or so back in the 1300s. Obviously these claims overlapped greatly.
In Macedonia, for example, Greeks claimed all Macedonians were Greeks because Alexander the Great was from Macedonia. In fact, I think they still do. To an unbiased observer, this is a really, really flimsy basis for such a claim.
Meanwhile, the Macedonians themselves were largely Orthodox Slavs. They spoke a language with various dialects that were close to Serbian on one end of the region and Bulgarian on the other.
So of course Serbs and Bulgarians both claimed all Macedonians were “really” members of their “nationality.”
This leaves out of the mess that people in the Balkans didn’t live in neat blocks by “nationality” as they (mostly) did in Western Europe. They lived in general in villages of various ethnicities scattered across the landscape. Which meant that when one “nation” acquired title to the area, the other ethnic groups imediately became intruders, in a land where they had lived just as long as their now “majority” neighbors.
What a mess!