It is not so much the conditioner gives false reading. Rather, the typical ammonia test cannot distinguish between bound & free ammonia.
Tap water typically contains chloramines as disinfectant. This is broken down to Chlorine and Ammonia by the conditioner. Both are bound to the conditioner and are harmless. Your test kit, however, will read the bound ammonia & give you a positive reading.
You will typically see less than one of ammonia in treated tap water. To tell how much free ammonia you have in the tank after your water change, you could do one of the following:
1. Use a salicylate ammonia test kit (a salt water ammonia test) - this will accurately read the free ammonia.
2. Treat a sample of tap water with your conditioner & measure the ammonia level. Then subtract that from your tank reading. Eg - If your tap reads 0.5, and you have done a 50% pwc and the tank now reads 2.0. The estimated free ammonia would be 2.0-(0.5x50%) = 1.75.
3. Wait 24 hrs - the effect of Prime would have dissipated, and whatever ammonia you read is true.
The simplest thing to do is "3". To prove that the tank is cycled, just make sure that the ammonia (& nitrite) are both zero BEFORE your water change.