Not exactly, it came from the Middle East or just maybe North Africa directly more than 8000 years ago. It is a Neolithic lineage which likely was mostly confined to Dalmatian coast from around 6300 BC until 2500 BC. So almost 4000 years of being there. Then something happened, the Steppe IE waves were beginning to arrive so out of the native Neolithic element Cetina culture was created. So the local remnants of Hvar culture embraced war, social stratification and other things that came with Indoeuropeans. Cetina culture died out without inheritors but it seems most of E-V13 that is CTS1273 were part of daughter cultures of Cetina: Belotic-Bela Crkva, Bubanj Hum III and Armenochori, and then likely Danubian complex. None of these cultures can be regarded as proto-Illyrian. In fact considering the fact that Minyan Ware was recorded in Bubanj Hum III they are far more likely to have something to do with proto-Greeks.. Except the successor of Belotic-bela Crkva and Bubanj Hum III, Vatin had a Western Serbian variant which was "illyrianized" early on.
So J-L283/Illyrians essentially took over the old E-V13 lands..
So you see as usual the hugely expanding haplogroups usually expand into their non-native area, they overgrow the native area and have to expand to other peoples lands!! J-L283 is not native to Western Balkan but it demographically boomed there. R-Z93 is not native to India but it boomed there. R-L51 is not native to Western Europe but it boomed there. J-P58 is not native to Middle East but it boomed there. E-V13 is not native to Eastern/Central Balkan but it boomed there...