The principal behind CO2 / oxygen in the water is gaseous exchange. At the surface, where the water meets the air, CO2 passes out of the water and into the air. Oxygen goes in the opposite direction and passes from the air to the water. (Actually, it is a balancing act and the concentrations of both CO2 and O2 balance out across the barrier that is the air/water interface. But the normal concentrations of O2 and CO2 in air and water gives the flows I've described above).
Agitating the water surface increases the surface area of the interface therefore speeds up the flows of gas between air and water.
For a tank that has only fish, which produce Co2 and consume O2, you want to get rid of the CO2 and increase the O2 as quickly as possible, so air stones and increasing surface agitation is preferred.
However, for a tank with a lot of plants, the CO2 that the fish generate during the day will be used up by the plants. At night, the plants stop using up CO2 and produce it. This is why I see the pH in my tank drop overnight (when my tank is correctly balanced), because CO2 reduces the pH of the water. (
@Sue has posted the technical explanation for this somewhere). So for a tank with a lot of plants, you don't really want to agitate the surface as it is generally better to keep the CO2 in the water for the plants.
The natural fluctuation of CO2 due to light levels changes is unlikely to trigger BBA on its own. It usually takes an external change to do this. That external influence could be a water change (if the level of CO2 in the tank has got very low) or turning CO2 injection on / off or changing the surface agitation regularly, or turning an airstone on / off. There are also other reasons and these may not trigger BBA.
At the moment I don't have enough fish in my tank to produce the CO2 that my plants would like, so the daily pH cycle isn't quite right. My preferred method for getting the right balance is to increase the amount of CO2 produced by fish (more fish!), also because this is more stable. My aim is to have the right balance between fish and plants so that fish produce all the CO2 that the plants need, no more, no less. But I have a lot of juvenile fish in my tank and what I don't want to do is be overstocked when they've all finally grown!