My parked car was hit by a Uhaul, now dealing with RepWest insurance

My parked car was hit by a Uhaul, the driver took responsibility and called Uhaul to let them know. They had purchased Uhaul insurance which is managed by RepWest and Uhaul told them that i would need to call RepWest and file a claim. I called my insurance first (Travelers) and they tried to call RepWest and handle it but were told that i need to complete the RepWest claim (sending pics etc). I now am assigned a RepWest adjuster, but i heard they're difficult to deal with and lowball claims, and i feel like Travelers should be handling all of this instead of me dealing directly with RepWest. Shouldn't Travelers be haggling with RepWest and getting my deductible covered through subrogation etc instead of me acting like an independent agent at the mercy of RepWest when i don't really know how to navigate the process properly? Thoughts?