OK. Once you get your API master test kit, we will have a better idea of what is happening.
I'm presuming you are using a dechlorinator on your tap water? What brand and product name? Your ammonia readings could easily be coming right from your tap water.
Depending on your pH, you may not be having any real ammonia issues unless your pH is above 8.0. If you have a low pH down in the low 6's, you could have 3-5ppm of ammonia and not have any problems. If you have a high pH in the 8's, even .25ppm can be toxic.
What are your numbers from your dip sticks? While they aren't highly accurate and can vary from stick to stick, if you've kept a log of their numbers, we can at least get a general idea of your other numbers.
Also, do a 48 hour tap water baseline test on your tap water... using the dip sticks so we can see what's happening out of the tap.
Here's a snip from my blog, "Find Your Tap / Source Water Baseline"...
Quite often you are told to test your tank water chemistry (parameters) for things like ammonia, nitrite, nitrate, pH, temperature, KH and GH... the basic tests that most fish keepers should have. Something you are not often told is that you should know your tap/source water parameters and what happens to your tap/source water after you fill your tank or do a PWC (partial water change). The pH will usually change a little or a lot. There may be ammonia, nitrite or nitrate in your tap/source water. The KH and GH could change or be non-existent.
To find your tap/source water baseline, you should run your cold water for a minute or two to flush out any stagnant water in your home pipes. Then fill a one gallon bucket or other open top container. You need a large opening to have adequate surface area. After filling the bucket, immediately test it for all of your tests (preferably the seven mentioned above). Record your numbers. Add your dechlor product. Test for ammonia again. Record number.
If you have chloramine treated water, when you add your dechlor product, it will break the bond between the chlorine and ammonia so you will get a slight ammonia reading. Normally, it's not more than 0.5ppm (which is easily converted in your biological filtration in an established tank but this level can cause alarm in a new tank depending on the pH and temperature).
Now set the bucket on the side and wait 24 to 48 hours and test the water again and compare the numbers. You could also test it at 24 and 48 hours to get even more information about what happens to your tap/source water once it gets into your tank during PWC's. You can speed up this 48 hour time period by adding an air stone to the bucket to agitate the water constantly. If you don't have an extra air pump and stone, then just stir the water regularly to increase the outgasing of CO2 and any other gases in the water that will outgas once in your aquarium anyhow.
Some tap/source waters have high CO2 levels out of the tap which results in a low pH right out the tap but then as the CO2 outgases, the pH stabilizes to a higher level. Other tap waters have buffers that raise the pH out of the tap but then these buffers wear out quickly when exposed to light, air and temperature changes and the pH will drop.
Also, if you have tropical fish and regularly add hot water to your cold water to raise the temperature to match the tank temperature, you should know what your hot water parameters are as well. Your hot water heater is basically a distillery that is boiling the water which causes the chemistry to change. Many of the additives to your water will come out of solution and settle in the bottom of your hot water heater. You will notice a faucet on the bottom of your hot water heater. Most people don't do this but you should partially drain your hot water heater once a year to remove this sediment. This sediment will eventually cause your hot water heater to fail. Also, it's not good for your fish. Usually, it's just a matter of hooking up a quality garden hose to the faucet, running it out your back door and then open the faucet to let the sediment and sludge flush out until the water is coming out clear. Read your owners manual or online sources for more information on how to do proper maintenance to your hot water heater.
To learn more about the water quality for your area, in the USA, check here:
http://www.epa.gov/safewater/dwinfo/index.html