I think it must have a fixed white balance, or the average hue captured would hardly change over time at all.
Adjusting the inside lights until the inside sensor is satisfied, rather than based on specifying in absolute units, would also have the benefit of taking into account any influence on indoor overall color contributed by your walls, window coverings, and anything else. Might need to average multiple sensors for best results, unless a single sensor does that through a wide angle diffuser.
This is a bit like how automatic audio equalizers (I think Sonos offers this, for example) don't work just by ensuring that the speaker delivers the desired frequency response curve (or lack thereof), but by actually using a measurement mic, since your experience will be influenced by the combination of speaker+room. The difference is that you only need to have the mic around when making changes to the room/furniture (which is rare) whereas you'd be making changes to the indoor light bulbs continuously (based on outdoor light), so you need your indoor sensor running continuously.