Hi all, You are fine, it isn't dying organisms.
When proteins are organically degraded they end as ammonia (NH3), this ammonia is then taken up by plants, or enters microbial filtration where it is eventually converted to nitrate (NO3). How quickly that conversion occurs depends upon a number of factors, but the time scale is always going to be longer than the hour. Nitrates are extremely soluble, so when you add them as chemical salts (KNO3 etc) you should get a very quick dissolution, and within minutes the water column will all have the same amount of NO3- ions.
The rise in readings will be to do with the test kit and probably interference from other ions. Monovalent ions are quite difficult to measure accurately, even in a lab.
cheers Darrel