Not necessarily. As someone answered in your similar question, your lender will receive your tax assessments and adjust your escrow account accordingly. What sometimes happens is that the assessment (which typically lags by 1-2 years, depending on your county/city policy for reassessments) was made prior to the new construction. Maybe there was an old house on the property that the builder tore down to build a new one. The assessment will show for, let's say, $350,000, even though the new house sold for (and will soon be assessed for) $700,000. In this case, you'll get a break for awhile, until the tax assessor updates the records and sends out the new assessments.
Also, note that your "house note"--your mortgage--will not decrease or increase as a result of a reassessment. However, your total monthly payment--PITI--principal, interest, taxes, and insurance--could be adjusted to account for the increase in taxes.
Hope that helps.