You need to pin the app to home screen and it would update your latest place weather every 30 minutes to every 2 hours. I found out some users are not able to see the Live Tile even though they have the app tile pinned in their home screen. Please make sure the Flat Weather background task is turned on from Settings > Applications > Background Tasks and find the Flat Weather and make sure the background task is checked and it's on.
If the background agent was on and you still cannot get your live tile after a while, please contact me with direct email from the Flat Weather about page > contact and send me your device detail and which country you are living. I will try to resolve the issue in next update.