Well first, I will attempt to answer this question by proclaiming that I am just using an extensive knowledge on the NBA, and a general love of basketball.

If this topic interests you - I would strongly suggest watching the ESPN 30 for 30 documentary "Once Friends" if you haven't already - it discusses the Yugoslavian National team during the split of Yugoslavia in 1991. Narrated by Vlade Divac, with help from other notable players from that great national team, Tony Kukoc, Dino Radja - Vlade takes you through that tension filled days when Croat Nationalism was at a peak, and eventually turned these good friends against each other (Kukoc, Radja, Petrovic were Croat; Divac was a Serb), it also discusses easily the most popular, best player from this era in the Balkans, and very possibility the answer to your question - Drazen Petrovic.

To the Balkans, Petrovic is the Michael Jordan of the era, also the reason why you will see a lot of Balkans today sign contracts with the New Jersey Nets (Petrovic played for the Nets before his car accident/death). Currently, there are three players from the Balkans on the Nets - and if you paid attention to the news, Steph Curry sent Petrovic's mother one of his game worn jerseys from the NBA Finals this year to put up in the Petrovic museum in his hometown of Sibenik, Croatia.

So I think when discussing basketball in the Balkans, and the popularity, you have to begin by taking a look at the impact of Drazen Petrovic as an idol to the area.

Hopefully this helped a bit.