The town sets up a budget. (as an example consider the following) They need $1,000,000 to run. They have 1,000 houses in the town all identical and worth the same amount.
If each house would sell for $10,000 they will have to pay $1,000 to fund the town.
If each house was worth $1,000,000 they will each have to pay $1,000 to fund the town.
The mil rate will almost certainly drop only after house prices rise enough to allow the town to take the same amount of money based on a higher house value. It makes no sense to think otherwise.
Even if the mil rate drops expect (in real life) taxes ($$$) paid to go up. There is no way to avoid it unless more expensive property comes into town without adding to town expenses.