This is probably another case of the display not being updated immediately under a specific situation. After a turn or two I looked at the domestic policy screen again and saw that the overall approval rate now tracks with the tax rate.
In line with this, if a planet is currently selected while the tax rate is being altered, the approval rate of a planet should also track with the spending rate immediately. With the current code, you either have to deselect and reselect the planet to see the affect of a tax rate change, or go to the next turn.