Croatia was always fully integrated in Austro-Hungarian (and coast into Venetian) cultural circle, which means that European cultural, artistic, religious and political developments reached Croatia quickly (humanism, reneissance, baroque, reformation, socialism and various artistic fashions...) and were quickly adopted. So Croatian upper classes dressed, listened to same music, preferred same architecture and arts like their Austrian, Hungarian and Italian peers. With, of course, some uniqueness, for instance fashion had more in common with Hungarian than Austrian ("Hussar" style) in the north, while Italian in the south. That means that whichever new fashion or new development or idea reached Venice, Budapest or Vienna, came quickly to Croatia. Italy and Austria are also the places where they went for higher education rather than France, Germany or England (which wouldn't make much sense as they're far away and not where a young Austro-Hungarian upper class kid would care to study when all the cool kids are in Vienna or Prague). Croatian, in fact Austro-Hungarian aristrocracy was very mixed and often owned land in different parts of the empire and would often integrate and assimilate into the nation they grew up in. So many German (Austrian), Czech and Hungarian aristrocrats became prominent Croatian politicians, artists, scientists etc, while many Croats went assimilated into wherever they went to live in other parts of the empire. In fact, this goes for all classes of population, there was a lot of migration and integration in A-H empire, and most of all in areas liberated from Ottomans which were colonized by people from everywhere.

The Balkan you're imagining, the alien Ottomanic Balkan begins in Bosnia and Serbia, with Serbia starting to integrate in European cultural circle (from Viennese source) soon as they gained inependence and in early 20th century you'd have painters painting same stuff in Belgrade, Athens and Niš as in America and New Zeland.

But bottom line is, Croats didn't need to go to study elsewhere to pick up on specific arts, this was our thing very soon after it became a thing because we're very close to the places these things originated and part of same society which enjoyed these things throughout Europe. Someone would see some new style of dress which (for example) came from France on a ball in Vienna and would have to have wear it on his ball in his castle in Croatia because his peers (who came to the ball from Graz in Austria, Pecs in Hungary and Split in Dalmatia) would expect it, same like any aristrocrat anywhere in Europe, and lower classes would immitate the upper like they always did.

edit: there weren't many wealthy industrialists in Croatia because there was very little industry before WW2 (compared to Austria and Bohemia, even Slovenia, not to mention Germany and France, but still more than in formerly Ottoman Balkans), Croatia and Hungary were agrarian half of A-H empire which itself was less industrialized than other powers, except Ottomans.