Yes the rise in ammonia is normal during the initial cycling. This is a result of the addition of material that is breaking down into ammonia. In this case probably fish poop and whatever you are feeding the fish. As the biofiltration bacteria grow in volume the ammonia will start to recede, nitrites will increse then recede, and nitrates will increase. The way you will evetually deal with the nitrates is by water changes.
Adam seems as though you may be lacking some knowledge in the workings of setting up an aquarium and specifically a saltwater aquarium. I would suggest to you to read the threads at the top of this page to get yourself familiar with how what and when things are going to happen.
The other suggestion I would make at this time is for you to;
1. Return the fish to the fish store and cycle the tank by other means. While it has been accepted practice with saltwater tanks in the past to cycle with "sacrificial" fish the hobby has come along and found more acceptable ways to do this. You are subjecting these creatures to the possibility of ammonia poisoning. Have a read here about that.
http://www.firsttankguide.net/ammonia-stress.php
2. If you are convinced that you will keep these fish for whatever reason I would recommend that you test your ammonia levels at the very least daily and have ready mixed saltwater available to do a water change when the ammonia level reaches 0.5.
With that welcome to SWF.com. Please do some more reading and feel free and encouraged to ask questions here prior to doing anything in your tank. Best to get as much information as you can before you make any decisions.
