Tokyo Girl: a very nice movie that goes across time, it's technically not a time travelling/flash back movie though (it's a cell phone that travels across time and makes communication across a century possible), but it's amazing in it's own way!
Faith: amazing time travelling drama!
I Hear Your Voice: probably less what you're looking for, but I'll recommend it anyway since it's such a good drama :P the main characters have met when they're younger (a bit like you who came from the stars) and the guy wants to find the girl again + the guy has a super power (also like Do Min Joon lol) that allows him to hear other people's thoughts.
hope it helps!
edit: oops~ I just saw that you put I hear your voice on hold, don't know if you want to pick it up again. I hope you do :3
edit2: and oops again, faith is also there. oh well :P I hope you'd still be interested in the movie ^-^