Marco was canoodling with a Chinese dude, lol ("not that there's anything wrong with it")
"Rosie" tells him in their first scene together that "she" was one of the Chinese laborers who built the track their train was on. We've already seen earlier in the movie that he and the other soldiers were brainwashed to see Chinese military brass as women (of their own respective races). I'm convinced that's exactly what's going on here.
On this viewing, I watched closely to see if anyone else ever interacted with, or even observed, the Janet Leigh character. The closest is at the police station, where there is a detective on the phone in the background, but presumably they just saw an Asian man coming to get Marco and thought little of it. We can assume the taxi driver saw them in the back seat together, but we don't see him. Similarly, in the train a railroad employee squeezes by them quickly.
Otherwise, all their scenes are just the two of them. In the passageway between two train cars, in the back of the taxi, at Marco's apartment with no one else present. He thinks he's engaged to this lovely blonde woman named Eugenie/Rosie, but it is in fact a Chinese agent hanging out with him the whole time. I suppose they could have given us a peek of his real appearance like they did at the "garden club meeting", but that might have squicked too many people out at the time for the studio's taste, as audiences would have realized Marco was actually kissing (and sleeping with?) a man.