If you're paying more in taxes it's either because the taxing authority decided to raise more money or your property has increased relative to your neighbours.
If your whole neighborhood goes up, but not the whole city/municipality, correct. If the entire tax base goes up (not just one neighborhood), you should expect the mill rate to fall.
Tax rates are generally changed by an independent political process (the municipal budget) which often has the power to increase/decrease the mill rate based on how much money is needed/desired. This doesn't change the fact that the mill rate does generally fall by a lot when properties are reassessed in areas that have seen a large property price increase.
