Those are polymer electrolytic capacitors, there is no liquid electrolyte to leak out, so it's definitely not the cause of the corrosion.
Something corrosive has been spilled on that board, and it has attacked the aluminum of the capacitor case.
With that kind of damage to the case, I would replace it regardless if it tests good or not.
As for the actual repair... all components in the affected area should be removed, then the pads and traces carefully cleaned up and inspected very closely. Liquid damage can be pretty sneaky, it can for example corrode the inside of a via, creating an open circuit that is very difficult to find visually. It will also eat away at solder connections, thus the importance of removing the components and replacing using fresh solder.