I found above mentioned relationship in river water. However, some studies report that the coefficient of correlation between ammonium-N and phosphate-P is higher in pre-monsoon and monsoon than post-monsoon.
If this is due to fertilizer run-off from fields upstream, you may need to look at land uses above the sampling site, dominant patterns of fertilizer use for the crops grown there, and the relevant hydrological drivers. If this is due to urban sources of N and P, rather than agricultural, then you need to look at these patterns (I don't know what they could be).
I would guess that the answer to your question lies with the specific rivers that people have studied. There are bound to be differences from one place to another. To take two extreme cases, I would guess that temporal patterns of N and P in monsoon-influenced rivers in India will be different from monsoon-influenced rivers in Australia; and a river running from densely forested headwaters in Indonesia will be different from a river running out of the plains in India. This answer is "off the top of my head" because I have never made these measurements, but I am not very surprised that there's a difference. I would be surprised if there are large inter-annual differences for any particular site on a specific river, and if it was so, I would look for a point source, rather than the expected non-point sources.