Generally, the correct preposition to use after interpretation is of. We thus speak of the interpretations of a Biblical passage, of a provision of the U.S. Constitution, of a dream, of a complex work of art. Generally, using on in place of of in such a context, can be dismissed as simply a mistake.
Why might one, nevertheless, sometimes want to use on in such a context? The key is that we sometimes speak of imposing an interpretation on something that does not obviously call for an interpretation. Somebody's actions (the OP's own example) may, at first sight, seem unremarkable, and then somebody may offer an account that purports to reveal something unobvious about their purposes—in such a case, we can say that an interpretation has been imposed on these actions. There is then a natural step from speaking about imposing an interpretation on the actions to speaking of it as an interpretation on the actions. Whether this step is to be welcomed or deplored is likely to be a matter of opinion, but it is certainly understandable.