Could you answer how many heads are included per zone? When you turn it on, and one zone goes off, how many heads are included? How many zones do you have on your controller?
Are the drip lines in a separate zone? I totally understand why you would be very very unhappy but these yayhoos deserve to be called out to fix what they do. If they DON'T fix it THEN you can hire someone else and charge it to the original yayhoo.
Your first step will be to call that yayhoo and get him to fix this problem he made. I would also call an expert from Rainbird to have them listen to your discussion with said yayhoo. Have someone right there that understands automatic irrigation, let them know of course you will be getting this fixed and you want a PROFESSIONAL. They'll be out there and should be professional. Saying nothing just listening. No trucks or uniforms with decals. You want to get information from this yayhoo and then get your irrigation fixed professionally. The laws are fairly clear; this yayhoo irrigation contractor needs to have a license, references, bonded...or he is in big time trouble. That you shall be able to use for power. With guidance from Rainbird or other referenced irrigation/landscape contractor you should be able to get your irrigation working without spending another dime. You could even have a professional dude right there while this yayhoo is supervised by a professional. I would also be talking with an attorney. Free for the first half hour? Scare the pants off this guy he has to make good or pay for someone who can, that is the law. If he isn't licensed don't let anyone shame you for not looking before hiring.
Not your problem until now but you deserve to have your irrigation working for the money you already paid. And yayhoo contractors, subcontractors, landscape contractors...need feedback when they take advantage of homeowners! There are laws for taking advantage of home owners by contractors whether licensed and especially unlicensed.
Angie's list is one way to get information. Preferably before you hire but if you've been hurt by a builder, contractor, subcontractor, someone hired by a contractor or subcontractor and every state has their own warranty clauses that unless you signed a contract that was amended in the favor of the contractor you have major major rights. Angie's List, lawyers, have ways to help you recover your money and get your job done correctly and getting it done using the money of your yayhoo. Regardless of whether you had a contract with them or asked for their license and bonding information.
You have rights and the statute of limitations can be HUGE. In Washington State, it is 12 years!