That seems odd. It's common for the pH of your tap water to change after you let it sit for a while. That has to do with oxygenation. But I'm not aware of ammonia doing that.
Your tap water likely contains ammonium - which is a byproduct of municipal chlorination. It's not as harmful as ammonia, but products like Prime don't remove it. So if your tank water has been sitting a while and there's been a lot of evaporation, the concentration might go up. But .5 to 2.0 is a huge jump, so that's probably not it.
Did you use anything to clean the tank or decorations that might have had ammonia on it? An old rag with Windex or some other cleaner? (If so, I'd rinse everything off, just to make sure you have no other chemicals in there.) Did someone give you gravel from an old tank to "seed" yours? (If so, there might be fish poop and debris in there that's temporarily raising the ammonia levels until your bacteria culture really takes off. In which case, cycling will take care of that.)
Other than that, I'd suspect the ammonia test itself. If you're using those paper strips, they're notoriously wonky... especially so if you get an old one that's been sitting in the store for a while. The ones with the drops and test tubes are more of a hassle, but they're more accurate.