What will my supplemental tax bill be?

My city has a property tax rate of 1.06%. I just moved into a new house in September. I got a tax bill (due in 2 installments) for a total of $1740. The bill indicates this is tax for the property only ($94,000), as the city records have not caught up yet. My house on the property is worth about $310,000. When I called the tax collectors office to ask what my supplemental tax bill would be, the lady laughed at me and said it would be at least 4 times my bill for property only (nice huh?). Is this correct? The way I figure, there's no way it could really be 4x $1740. Help!