Luke: For some reason the Powers That Be'ed (tense? lol) decided that children in English schools didn't need to learn English grammar. You, as a European learning English as a secondary language, got that benefit. I can't, therefore, say whether you're right or wrong to claim "logging out - no tense".

Let me ask you, though, what tense is implied by:
Action: Logging out

Regardless of any technical terminology, that, to me, is clearly in the present tense. Other interpretations may be possible but any strength for them is very low - in the sense that with the word "ball", for example, people are far more likely to assume spherical object rather than to gather into a roughly spherical region (eg. planetary debris balling together to form an astral body, or balling wool).

And it's fine if you disagree, for that will highlight my original point that "Logged out" is better because it's unambiguous.
;-)