After the inflationary era the Universe became radiation dominated. The era of radiation domination is defined as the phase during which the temperature of the Universe was so high that the kinetic energy of the massive particles in the Universe were too large compared to their rest masses. If I understand it correct, as the temperature dropped, the radiation dominated phase ended when ultrarelativistic particles became nonrelativistic. Now, here is my problem. Clearly, with the decrease in temperature, the class of heavier particles (e.g., some heavy dark matter) will become nonrelativistic much earlier than the class of lighter particles (e.g. electrons, quarks etc). On the other hand, photons and neutrinos will (almost) always remain relativistic.
$\bullet$ How do we pinpoint the time at which radiation domination ended and matter domination started?
Response after @Cham's answer:
$\bullet$ If particles with different masses become nonrelativistic at different times, how can there be a unique time for the onset of matter domination? I would like to have a physical understanding of when this transition happens.