Automatic Scrolling to the Top of the Timeline in Twitterrific (iOS and macOS)

Can I make the timeline automatically jump to the top at refresh?

No, the timeline always maintains its position for easy reading. However, on iOS, you can tap the device's status bar (with the time) to manually scroll to the top instantly. On the Mac you click the icon of the currently selected tab to toggle up to the top of the timeline (and back down) if you wish. You can also press the Home key on both platforms to jump to the top as well.