No, it doesn't mean your taxes will go down.
I can't specifically address your area. But, in general, the assessed values of properties will go down when surrounding sales justify it. So it's very likely that your assessment will go down.
However, that absolutely does NOT mean that your taxes are going to go down. Your taxes are based on two items: (1) The assessed value, and (2) the tax rate. Often, in order to offset declining valuations, localities will raise the rate.
Here's an example. Suppose a home is assessed at $100,000. And suppose the tax rate is $1 per $100 of assessed value. In this case, the taxes on the home would be $1,000 ($1 x 1,000).
Now the assessment falls to $90,000. IF the tax rate remained at $1 per $100 of assessed value, your taxes would fall to $900. However, in order to maintain a steady flow of revenue, your taxing authority might raise the tax rate to $1.10 per $100 of assessed value. Now you'd owe $990 in taxes. Pretty much no change. Or suppose the taxing authority raises the tax rate to $1.20 per $100 of assessed value. Now you'd owe $1,080 in taxes, an actual increase in the amount you'd have to pay.
So, pay attention not only to your assessment but also to your tax rate.
Hope that helps.