Don't know if this would give you the look you want, but when I did my entryway I left the baseboard molding on and tiled up close to it. I then put quarter round molding on to cover the gap and finish it off. Looks good to me.
If after seeing your photo's and video's, and instead of apologizing profusely, he asks so whats going on?, it leads me to believe this company is a S#*t show. I guess you have to give them a chance to make it right, but man this kind of stuff pisses me off.
You don't have a rain sensor tied into the controller do you? I know mine won't come on if I get a certain amount of rain. I'm not even able to manually turn mine on unless I bypass the sensor.