The two make a coincidental encounter in late night Tokyo, but how did Tanjiro recognize Muzan while walking around?
Tanjiro was able to recognize Muzan through his scent. While on a mission in Asakusa, Tanjiro picks up on the same scent that destroyed his family. Realizing Muzan is in the area, Tanjiro gives chase.
He was able to remember the scent left behind at the Kamado family massacre. Once it comes up again, Tanjiro is able to successfully recognize Muzan and approach him.
Tanjiro recognizes Muzan in Asakusa
In chapter #13, Tanjiro’s crow instructs him to head for Asakusa in Tokyo. Rumors tell of a demon hiding in the city, with no time to rest in between missions.
Two days later, Tanjiro arrives at Asakusa. He’s awestruck by the architecture and use of modern electricity. At risk of passing out, he grabs Nezuko and heads for a Udon Cart to eat and relax. Nezuko is actually able to survive without eating.
Just as he notes the vast population of the city, Tanjiro focuses on a smell. “That smell,” Tanjiro says. “Why here?!”
Tanjiro bolts off in the direction of the smell, recognizing it as the same scent which lingered in his home after the massacre. He pushes through the crowd before placing his hand on a man’s shoulder.
The man turns around. It is Muzan Kibutsuji, the King of Demons and the one responsible for destroying Tanjiro’s family and turning Nezuko into a demon.
Tanjiro reaches for his sword but stops at the sight of a young girl in Muzan’s arms. Realizing that Muzan is masquerading as a human, fake family and all, Tanjiro freezes up. He picks up a human scent on Muzan’s family members, questioning if they’re aware of the demon’s true character.
Muzan plays it off casually. He claims Tanjiro is a boy who mistook him for someone else. As the Muzan family walks away, the Demon Lord slashes a nearby civilian in order to create confusion. While the person transforms into a demon, Tanjiro’s hands will be full as Muzan escapes.
So that’s the answer. Tanjiro was able to recognize Muzan through the power of scent.