The conversion of light into electricity happens pretty much instantaneously. Well, it takes time, but such a short amount of time that we can't perceive it without some serious instrumentation.
So if the insolation on the panels themselves at one second is 500W/m², and your system's efficiency is 20%, you'll get 100W for every m² of panel in that second.
If cloud passes over and insolation halves to 250W/m² for ten seconds, then your power will also halve for ten seconds (assuming it's a small installation, so that the entire array effectively experiences the same cloud at the same moment).
For grid-connected systems, this doesn't really make any difference: the rest of the grid acts as a massive storage buffer that smooths everything out. So in general, the number that interests people is how much energy will they get on average per day on an average day of the year. The system designer still has to account for the maximum generation at any one moment, to pick the correct inverter.
If, however, it's a standalone system, not grid-connected, and so does not have the luxury of that storage buffer, then it usually has a battery connected: that battery provides the smoothing. But now the system designer needs to do an hour-by-hour calculation for, say, 3 years, as well as accounting for peak momentary power in and out, to size the battery (and inverter if required) correctly for the application. As the battery is going to store enough energy for at least several hours of load, the modelling doesn't need to be any more detailed than hourly. But if the particular application had little or no storage, then you'd have to model down to the level of individual seconds, or possibly even sub-second intervals, to get a correct system design.
