Answers

It depends on the faucet and whether the faucet has an aereator. Even when the valve is turned into the off positions, there is still some residual water in the faucet, and aereator. Once all of the water on the room side of the faucet has drained out, the dripping will stop. 

Jie, 

Since you are not getting satisfaction from your builder, I would take all of your documentation to your city or county permit office (call ahead to determine who to speak with).  Standing water in any developement is unnaceptable and the municipality may require them to fix it. 

If the local governement can't help, contact an attorney specializing in land or propery law and ask them to send a letter to the builder.  Spending a few hundred dollars for this may go a long way. If you have to go to court, I would do so. 

My neighbors and I had sanding water and grading problems that we were able to demonstrate to the builder, and the builder came out and put drains in, no questions asked. We did not have to go to the county or hire an attorney. They recognized the problem and fixed it. 

Good Luck!