Principle of universality is one of criminal law's principles that deals with scope of court's jurisdiction. This principle is connected with international criminal law and means that every state is obliged and allowed to prosecute and punish perpetrators of crimes under international law (e. g. war crimes, piracy, crimes against humanity etc.), hence every court is authorised to punish a perpetrator regardless of his nationality or of nationality of a victim (principle of personality) or of place where a crime was committed (principle of teritoriality). In other words according to principle of universality a court has jurisdiction even if the crime was not committed on his territory, by its national or against its national, because it is a crime which is by nature against values of international society as such and it's perpetration is of international concern.

Natural law as such is for me quite abstract concept and I prefer rather inclusive positivistic approach (Hart). Before we could discuss topic of their relation to natural law, we should define what natural law is and if it is indeed an existing "thing". But maybye answer lays in that natural law is something that obvius, that we can find it across the world. An example of such value is e. g. the value of peace and the desire for peace is inherent for any person and it is reflected also in values of international society that therefore considers crimes against peace/crime of agression as something naturaly wrong that should be punished despite of the law where a crimes were committed or of the law of perpetrator. Its criminal nature derives directly from international law's rule and it is therefore not a breach of legality pricniple (nullum crimen sine lege) - why such rule is part of international law? Because members of international society decided so. Why they formed and agreement on this topic (explicitely by int. treaty or implicitely in int. custom)? Maybye just becasue its "evil nature" derives from natural law and is hence evident to everyone. You didn't wrote anything wrong in your answer, it is just another point of view. Less juristic, more philosophical. Your approach was very important in times of Nuremberg tribunal that was first in the history that prosecuted these crimes and there was a question if such rule emerged yet. I would say that important is the outcome - to prosecute "evil people" and intuitively everyone knows that such crimes are wrong, but we need an rationalisation for doing so.