Yes, you would have to pay taxes on an assignment fee, too. That wouldn't be a capital gain, so it would just be ordinary income.
As far as when, at the least you would need to pay quarterly tax payments in order to avoid penalties at year end. Maybe the title company would withhold the taxes, I'm not sure.
Since you're asking about taxes, do some searching and read up on "self employment tax". If you're self employed, any income you make, like assignment fees, is subject to SET. That's social security and medicare. As an employee, you pay half of this tax (about 7.5%) and your employer pays the other half. When self employed, you pay both halves.