I've worked on the same problem and came up with the same solution. My password was "Teapot Dome" from 2016-2018, and it's been "Cottage Cheese" since then. I have just come up with a new password, which I obviously won't share.

This solution doesn't actually work. Maybe the people are mind readers rather than time travelers. Maybe they beat the password out of you and then wiped your memory. Maybe they are time travelers, but it's like Groundhog's Day rather than Back to the Future and they've guessed ten billion passwords until getting it right. Maybe they have an Infinite Improbability Drive and just got really lucky.

Your test can prove that something funky is going on. It can't prove that the something funky is time travel.