my friend translated it for me, so this is as much as i remember.

IU’s grandfather gave IU his workshop before he died, along with a doll he built (Hyunwoo) but he’s asleep. The doll will only wake up when he dies to take over the shop. So, IU’s waiting for the day he wakes up but can’t because she starts falling in love with him. She makes a time machine in order to go to the future to see him once he’s awake. When she travels to the future, Hyunwoo wakes up and sees her leave, so they never technically met at this time and dimension. So in the future, she works in a shop, and Hyunwoo visits the shop as a customer. And they meet at the time she drew on his wrist (if you payed attention to the time she drew and his watch) and yup , they meet in that time.