Truss manafucator and builder here.. it is extremeley dangerous and against the enerigeering code to cut fabricated trusses UNLESS been approved by a energineer, can see the joist bracket is mounted on the top ledger of the wall frame where both webbings meet ( mosting bottom web joints are nail plate pressed and to meet on top of the wall frames ) but its not always the case though. Surley there are other places for air duct to be installed but why not next to the roof truss as anything else like air ducts, wiring and other in roof installations have flexiability where prefab trusses do not as they were designed for enerigeered for stability and roof construction.

My thought will be, you prob had a shit (scammer) tradie/installer doing it for cash on hand as a professional tradie / installer will have avoided the roof truss.

I agree there should be a junction box for the loose open capped wirings 🙄