When Naruto meet his father Minato's Chakra inside of him during the Pain fight, why didn't Minato tell Naruto how Obito's Kamui works?
Minato's appearance merely a safeguard
When Minato sealed Kurama within Naruto, he sealed some of his chakra within Naruto as well. This was a countermeasure to assist Naruto re-seal Kurama if he were to ever to escape. This happens during the Pain Assault, and Naruto nearly breaks the seal out of anger.
With Minato's chakra being limited, he only had time to do what he needed to do, which was:
- Tighten Karuma's seal
- Give Naruto a summary of what he has observed up until now
Under Minato's observation, Pain was a simply pawn of Tobi. So why didn't he tell Naruto at this point?
Minato did not know Tobi was Obito
During Obito's assault on Konoha, he and Minato clashed. At this time, Minato did not know he was fighting Obito and assumed it was Madara. Obito was pronounced dead long before this, so Minato wouldn't have thought twice about this masked man's identity.
Minato does not come to the conclusion that Obito was the one who assaulted the village until their second clash during 4th Shinobi War.
Minato may not have know how it worked
Why would he know? Obito and Minato's clash during the Konoha assault was very brief. During the 4th Shinobi War, it took Kakashi some time to figure out how Kamui worked. And this only was because Kakashi noticed that Obito's sharingan prowess worked very similar to his own.
Minato didn't have anything to compare against to understand how Obito's abilities worked.