Keep checking your ammonia levels. As mentioned, it might be a bacterial bloom of heterotrophic bacteria. Heterotrophic bacteria feed off the organics in the water, but the problem is they convert that into ammonia. And they do multiply/reproduce and convert faster than nitrifying bacteria can keep up with, so elevated ammonia levels are usually present. Pretty much a mini cycle, just got to give the filters time to grow more and convert it all. But again, the elevated ammonia levels are present.
Keep a eye on the fish. Are they showing any signs of ammonia poisoning? (flashing, red gill tissue, deaths, overall look in bad shape, etc). If they are, then you definitely need to do something to reduce ammonia levels (water changes, Prime, ammo-lock, add Tetra SafeStart, etc)
That is assuming it is indeed a bacterial bloom.
Some substrates can be dusty and kick up the debris when disturbed (but don't create heterotrophic bacteria) and just takes some time for the light particles to settle to the bottom again. However your gravel is not one that is "dusty", so that is ruled out.
I have heard of some other precipitation causing cloudy water (harmless), but I do not know much in that area. Maybe that is it if you aren't having issues with ammonia, nitrite levels.
If it is just light particles being suspended in the water, a well circulated tank, with micron (or use cheap polyfil) in the filter can filter out the little particles from the water column.
After cleaning a dirty filter, it can dislodge a bunch of little particles and they would recollect within hours-day.
Just to make sure, did you clean the biological filter media with dechlorinated/aged tank water? Or did you use water straight from the tap? If you used tap water, you may have killed off too much beneficial bacteria which could lead to ammonia spikes (cloudy water as well). Also a tip, don't clean or replace more than 1/2 of your filter material at once (you never know what may be containing a important amount of necessary beneficial bacteria).