I have to admit, I'm surprised that you should ask this question. Of course you can demand that! This is YOUR money you are paying for that house! As a matter of fact, all building materials used in this construction have costs and labor units associated with them. Your builder has to take the cost of those drops out of the total price of the house if you say so. Now, the question is whether or not the credit is going to be worth installing (4) new TV and (4) new phone outlets, if you know what I mean. Also, I've found that builders would normally OK the owner hanging around and terminating or even pulling some cable. It may be too big of an undertaking for you alone to pull 58 cables around the house, and this is where you can make arrangements with your current builder if you trust them AND they can produce a proof of some education they've taken in the field, such as a BICSI Registered Installer certificate. If your builder does not have such a certificate or, alternatively, cannot have you meet a satisfied homeowner they built a home cabling system for, look for an outside contractor. Your current builder may like it or not, but, as long as the company you choose has low voltage licenses, required in your state, they should honor your choice and cooperate with your cabling contractor.
The absolute best time to start pulling the cable is the same time your electrical wiring goes in - when the framing is up, and the drywall is not. Therefore, make sure you act soon enough because it may take some time to find a couple of good contractors, discuss all the details of your system with them, and still have enough time to receive competitive bids and consider them.
Good luck with your project! I will be delighted to hear from you on different stages of your project, and maybe even get some pictures from you if you will have some time to drop us few messages.
Dmitri Abaimov, RCDD