Sounds like you experienced a time travel ripple. I don't know the proper name for it but basically the person in the suit was one experiencing early time travel. Problem is, while the person in the suit would have traveled properly, you were caught in the wave and it transported you as well.

As this would count towards evidence of time travel existing, they had to fix the timeline to where you never had that experience.

This lead to both experiences of you having traveled through time and where you lived life normal, to both happen but you're on the fixed timeline. Time is a funny thing though and glitches can allow information to transfer. It's hard to explain in words.

Basically you got time traveled accidentally and then the time travelers fixed the timeline so you didn't time travel. You're note traveled over as soon as time caught up to the same moment.

The one in the suit is probably keeping an eye on you to see if you show any chance of exposing what happened. I suggest not confronting them otherwise they will have to try and fix the timeline again. Or who knows, maybe only certain people can have experiences that leaks information through timelines and if they discover that you are one of them then they may attempt to recruit you.