ISI, or intersymbol interference, means different things in the context of PSK and OFDM signals. In PSK signals the symbols almost always have tails that extend, in the time-domain, into the times of other symbols. This is what they mean by "intersymbol interference".
Unfortunately they have to do this to reduce the bandwidth of the signal. They eliminate the negative effects of intersymbol interference by very carefully shaping the symbols so that when the receiver filters them through a matched filter, the other symbols have zero output at the sampling times of the other symbols.
With OFDM signals there is no overlap in the time-domain between symbols, so there is no intersymbol interference in the PSK sense of the term. What they mean by ISI in the context of ISI is when time-delayed multi-path signals cause the time-delayed symbols to overlap with the following symbol in the non-delayed signal. The cyclic prefix is added to the symbols to give the receiver enough un-corrupted data to recover the signal.
For instance, let's say that there are 64 sub-carriers and when we FFT them we get 64 samples of time-domain data. Let's also say that we think the worst multi-path we will generally see will be a time delay of 7 samples. If we make the cyclic-prefix 8 samples long then we should always have at least 65 "clean" samples, which gives us enough to recover the symbol.