Flew IAD-DXB-KBL last month with numerous colleagues, with the last leg on Safi (connected to the 3am departure, not a fun 8hr layover). My bags at IAD were tagged all the way to KBL, though one colleague traveling with me had to remind her check-in agent to tag the bags all the way through - I did not.

Try not to lose your baggage tag stubs (stickers agent hands back), as you will be asked for them when you check-in for your Safi flight (Safi check-in desk in the transfer area opens 3hrs before departure). One of my colleagues lost his and was told that due to that, it wasn't guaranteed that his bags would make the flight. Fortunately they did, along with my and all my colleague's bags, but best to avoid taking that risk.

It was a nice flight on an ex-Croatia Airlines A320 (warning stickers all in Croatian and English, and I even received Croatia Airlines sugar packets!). Have a safe trip to KBL!