If you don’t mind me sticking my nose in, the tzadik was born with a yetzer hora but killed it thorough his avodas Hashem.
DaasYochid, this is true.
But how is it killed through avodas Hashem? Because he brought himself to such a great level of devotion, love and connection with Hashem (which is only possible for someone who was born with a neshama that’s able to reach such levels of refinement) – that he lost all desire to go against Hashem by sinning (“yetzer harah”).
That’s why even according to Tanya, the main way of recognizing a tzaddik is a person who stands out in his holiness and devotion to Hashem. The temptation question is only an outcome of this general holy state, and probably not very recognizable to other people, as Yankel pointed out.