There's no banner ads in the paid version. You might be still looking at the free one.
Downloading the paid app does not remove the free app from your device. You might still be running the free version and it apparently doesn't know you already have the paid one and would still show ads and ask for upgrade.
The paid version has a brighter white cloud symbol on the icon, while the free version's cloud symbol on the icon is rather plain blue(see below). Please, make sure you're using the one with the white cloud on the icon.