From the engineering point of view (my tin ear doesn't care much)

Intonation is a compromise to adjust for the change in tension when you stop a string. In theory each fret should be adjusted for each string, but that's not very practical so the string length is adjusted at the bridge.

If your guitar is set up for standard tuning then you would 'expect' it to be wrong when you tune a string down, because you are changing the tension in that string.

Get your guitar set up for the tuning that you are using.