The NextPVR addon doesn't do the playback itself - it effectively just tells the Kodi the list of channels and recording, and URLs it can use to stream the data from, then Kodi takes care of the playback itself.
It's probably some setting in Kodi, like deinterlacing, that isn't working correctly with your hardware.
Are you using Kodi on Windows, or something else? (I'm no Kodi expert though, so won't really be able to advise what settings to try)
Most devices have trouble with 1080i so like sub wrote you will need a device that supports h/w deinterlacing. If your laptop and your device are using wifi that will be a big issue too.