Notifications are commonly considered a distraction when they arrive during a task, and consequently, prior research has consistently sought effective ways of deferring their arrival until task transitions. However, many smartphone users still interact with notifications during tasks. In our qualitative study combining diary study and semi-structured interviews, we examined 34 research participants' motivations for interacting with smartphone notifications at different times, including during tasks. Our findings resulted in a human-notification interaction framework comprised of 12 unique motivations frequently associated with three activity timings for interacting with notifications, including before-task, during-task, and after-task. Notably, participants frequently perceived interaction with notifications as a tool for improving task performance, making the most of their time, and promoting personal well-being, rather than only as a distraction. The before-the-task timing, in particular, has received little attention in previous research and deserves more attention as it was related to specific user motivations for notification interaction.