Capital Gains Taxes Above 250k

[Seattle Matt]

So I'm about to sell my primary residence, if the profit is roughly 450,000, and I am eligible for $250,000 capital gains exemption, it means that I will be paying capital gains on the remaining $200,000.

My question is this: in this scenario does that mean the first $250,000 counts as income which puts me into the tax bracket for 20% capital gains? Which means anytime someone takes the $250,000 exemption, any remaining capital gains would always be 20%?

Am I missing something here?