Actually, they're not always. It's not unusual for the Bat characters to just sense that something is true and go after it. What's ironic is that when Tim was talking to everybody else he just talked about how he "knew" Bruce is alive without giving any explanation--and even if he was right he was also acting like somebody who had seen so much death he couldn't handle it. Even here he's referring to himself "givin up on" Conner by accepting that he was dead. But here, in speaking with Conner, he doesn't sound crazy at all. He's talking about how he doesn't know what the thing that shot Batman did etc.
Not that that's the only reason Conner believes him--it's much more of an emotional thing. It's just sort of funny that Conner's also the only person he's presented with some form of factual reason for thinking Bruce is alive.