He was aware he needed to report it, but it was very late and he didn't have his phone to do it, so he figured he'd do it the next day by going back to the other world with his gear to get his phone and then come back to report on the issue. Seems logical enough to me.
Also, you seem to forget that several hours pass from the massacre until he's back to his world. In the previous chapter, there was nothing ice cold about his behaviour right after the massacre when he had just managed to escape to another world and he had to be comforted by the girl. (I won't say that he has the most natural reactions but a lot of things are awkward in this manga.)
As for telling lies, I would say that anyone in their right mind would want to avoid revealing to anyone else that they have a skill that allows them to travel to and back from another world, to increase their stats and then tamper with their status. Most people don't behave in a comically exaggerated way when telling a lie.
But honestly, I think that this agency is nuts. Like, these two dudes from the agencies apparently headed to investigate a missing person report at 23:00, then went inside the dungeon (which means they must have some competence as adventurers), recovered the bodies, did all the autopsy work, and first hour of the next day they're in front of his door? Then they proceed to interrogate him, test his status and they still have to file a report on the incident. If it was different people going for the rescue from the ones doing the investigation, I would understand, but this is absurd. I would not want to work for that government agency.