Spoilers Through Season 3 Episode 10, Protocol Omega.
In season 3 of Travelers, Jeff and Carly’s series-long battle finally ends with Jeff being taken over as a Traveler. Later, the Traveler who’s using Jeff as a host, 5416, suggests that the Director only took Jeff because Carly stood her ground during an argument and turned it into a kill or be killed situation, forcing the Director’s hand. In other words, he accuses her of causing Jeff’s death by making the Director choose between allowing both her and Jeff to die, or using Jeff as a host.
During the same conversation, 5416 makes it clear that he knows little about Jeff as a person or his history with Carly. Over the next few episodes, it becomes obvious that his training was lacking in other ways, because the future is getting worse, instead of better. His supposed “calling out” of Carly for causing the Director to take Jeff as a host, when it otherwise wouldn’t have, is based on ignorance, and should be dismissed.
When evidence from all three seasons is examined, it’s clear that the Director planned to use Jeff as a host, and planned to use him for this mission. Indeed, 5416 acknowledges that he’s been training for this mission, and has had training to function as “Jeff”, just not enough.