It is known in the literature that a phase transition to deconfined quark matter can trigger a core-collapse supernova explosion in otherwise non-exploding models. However, until now this explosion mechanism was only shown to be working for equations of state that are in contradiction with recent pulsar mass measurements. In this talk I will discuss that this explosion mechanism is related to the existence of a third family of compact stars that is present only in the hot, early stages of their evolution. Its existence is a result of unusual thermal properties of the two-phase coexistence region of the PT which furthermore can be related to the slope of the PT line in the temperature-pressure plain. If the PT does not lead to an explosion, there still could be another interesting effect of quark matter, namely a special, “inverted” form of convection.