Kape is correct. Tailor effects aren’t supposed to alter typecheck results, but Assassin under a tailor effect returns as Physician for whatever weird reason, so you hit a tailored Assassin and viewed them as Support to a typecheck. You’re not immune to tailor effects as EK using Allies (in fact, no investigative ability is immune to tailor effects unless performed by an empowered Investigative class), although a tailor doesn’t stop EK Allies from finding the target as a member of the scum faction.
P.S. By the same token, typechecking a Timesnatcher while they use Dark Dimension will return Investigative, since the Timesnatcher erroneously displays as Princess while under the tailor effect.