I used GameMaker: Studio for this so unfortunately what I can do to fix the issue is very limited, but I'm still pretty sure that the issue isn't just with higher refresh rate monitors since several others played the games I made with the same engine before. I'm pretty sure that at least one of them would also have a higher refresh rate monitor.
I even found a forum thread someone asking if that would happen and everyone's answer seems to be no: https://forum.yoyogames.com/index.php?threads/v-sync-question.40821