Correct, you pick two colors that you will play (e.g. blue and red) and then the AI plays just the parasites of the two other unchosen colors (e.g. green and yellow). In this example, the blue and red parasites would not be in play.
They will be in play as your own parasites which can become hyperparasites (and eventually parasites if the original AI's parasite has been consumed). In this way you can have multiple purchases per turn because cubes on (hyper)parasites count as organs for going macro or going terrestrial so it can benefit you indirectly.