Why does photosynthesis occur even in blue light when the photocentres are activated in red light
While it is true that strongest activity of Photosystem I and II happens with 700nm and 680nm light, these are not the only wavelengths that can be used for photosynthesis.

The green color of plants comes from chlorophyll, which is the main light absorbing component in the photo systems. If chlorophyll had only a single absorption peak at 680-700nm, it would have a blue(-ish) color instead of a green one.

Looking at the absorption spectrum of chlorophyll (which wavelengths it can absorb how well), you can see that there is a a second peak around 400nm:



This both explains the results of Engelmann's experiment and the green color of chlorophyll (with both red and blue colors removed only green remains)

Picture taken from: http://hyperphysics.phy-astr.gsu.edu/hbase/Biology/ligabs.html