They are not inconsistencies. They are in different dimensions - different versions of the same reality. It has nothing to do with timelines. I could create another game based on yet another dimension, another version of earth where technology is highly advanced with aliens and humans living peacefully together. Rin (a dream angel from Serenity) has the ability to jump to other dimensions. She shows up, and meets that dimension's version of "Mike". Now she knows three versions of the same person.
Now, want more confusion? Celeste is from Sylphine (yet another dimension)... Melody is from Seaside (another dimension). And all of those dimensions have one thing in common.... you. The person reading it. Hopefully you're picking up on what I am doing. I'm basically saying that we, the ones who read these visual novels, live in all of them. So when you play Last Human, you actually get to see someone from Serenity. When you play Serenity, you get to see someone from Sylphine.
Anyway... they're not inconsistencies. If they were, I'd be a pretty shitty writer LOL. It might be 1:00pm in Serenity but Rin jumps over to the Last Human dimension and its midnight there. So it has nothing to do with timelines at all. Hopefully you understood all that (and I didn't confuse you even more) :)