The ability reads SHE is immune, however, what about Terror affects that'd add another doom token, for example? In that case, the Terror effect wouldn't directly target her, would her immunity still cancel the effect. Or if an effect states All investigators lose 1 sanity/stamina/trophy/etc. Would the other investigators still be affected.
Kate Winthrop's ability should be played as if the terror die does not trigger the terror effects. So, no doom should be added, nor other investigator should suffer any effects. I could not find rules about that anywhere, but that's how things work in the mobile version of the game.