Will backup images be stored on my own server?
The backup is stored on your own server, yes. And this means that as long as you keep the backup on your server there will be more disk space used.
You can choose to have the backup active (recommended) or not: you can find the setting on Settings > ShortPixel > General.
If you notice that the backup folder uses too much disk space on your hosting account you can choose to remove it. We recommend you though to make a copy, via FTP for example, of the backup folder so you can restore any image in the future by just copying the backup folder back to your hosting account.