Likely monochloramine. Based upon my unscientific research, it goes like this:
Test tap water is positive for ammonia (because it is detecting the ammonia molecules that are part of the monochloramine). Then when you use the de-chlorinator, it separates the chlorine and destroys it (possibly by converting it into cl2(g) - not too sure on that one but nonetheless) in the same way as if it was just chlorine but then the ammonia molecules remain (may be NH3 or NH4). The test kit at that point detects basically the same amount of ammonia because none has been removed.
I found this out when my tap tested positive for ammonia. It made doing a fish-in cycle seem less practical because you're always adding ammonia. Prime says it 'locks' the ammonia away from the fish so I always use that during water changes rather than regular dechlorinator. In my tap it seems to be a pretty low concentration at about .25 ppm but unless something else is there to remove it (bacteria colony or special filter media), it just goes up with the addition of fish and other waste.
Using products to clean out the ammonia seemed like it would 'starve' the cycle I was trying to build by taking out the fish waste also and leaving no ammonia.
I guess if you are doing fishless, consider it another (secondary - .25 is low) source of ammonia, once you have a cycle, the ammonia added by water changes with tap water will be eaten by the bacteria very quickly during the Prime 'lock' phase. I think 'ammo lock' does the same thing. The trick to this is, however, to have a cycle already going.
If you are doing a fish-in cycle (as you said you were), you might consider using a separate filter in a bucket where you can use ammonia absorbing media in the filter and filter the tap water after conditioning it but before adding it to the tank. Or use that media on the main tank after water changes to reduce the amount of ammonia but remove the media soon so that the ammonia doesn't bottom out before the tank has cycled. That way you could keep your levels low while you fish-in cycle.
It looks like you are at 4ppm monochloramine as of 2010 but I don't know what ppm that translates to of ammonia after you have treated the water with conditioner. I suppose it also depends on how much ammonia you are detecting. EDIT - oh, .25 from LFS. OK, that's not that high. You certainly shouldn't need to treat it specially before partial water change once the tank is cycled (use Prime of course). As noted above, there are a few choices in the interim. My bet is that LFS will find ammonia in your tap water as well. edit - looks like yea they did.
Prime says it de-toxifies the ammonia, meaning that it is not toxic to the fish while it is 'locked' - but it is somehow still there and the test kit will pick it up if it is testing for NH3 and NH4. So its not a false positive, its positive for a NH compound that Seachem Prime says is 'detoxified' not 'gone.'
Also, I have had very good luck recently with both API QuickStart and Tetra SafeStart (check expiration label) to jump start the cycle. People will say it works or it wastes your money but I haven't seen anyone say it is hurtful to the livestock so make your own choice. You probably can't use it to have an established aquarium in one day appear just by pouring in 3 ml of milky looking chemies, however, it sure seemed to push my cycle along when also trying to do the other things right at the same time (and failing at some).
-sorry for all the ninja edits there