A the end, how was RAMBO 100% sure that...

They have a psychic connection. (He trusts him.)

Tell me something... are you fellas really with the Internal Revenue Service? - The Omega Man

I always assumed he saw the mercenaries put the gun to Trautman's head in the chopper.

He even says at the beginning (12 minutes in, when Rambo tells Trautman about the lie from Murdock about the 2nd Bataillon) "you're the only one i trust" and that trust exists for a reason. Trautman was a lot like a father to Rambo.

The radio transcript read to him in the torture scene vindicated Trautman.

The Job Interview Poem https://youtu.be/MtkmC4kCSTs

Trautman is the only person on earth that Rambo trusts. Rambo never would've believed for a second that Trautman double crossed him. They shared a warrior's code and camaraderie through Vietnam. Trautman was a father-figure to Rambo.

Also, Rambo already knew before he went on the mission that Murdock was dirty and couldn't be trusted so when he's betrayed it definitely wouldn't have come as much of a surprise.