Which ancestor? I'm a mutt of several different European ancestries, I don't speak a word of even modern Polish, Italian, or Albanian, let alone any archaic dialects, so I doubt they're going to be able to sus out that I'm a time traveler, what they do make of me is up for debate, probably nothing good but I doubt they'd land on time traveler from the future. If I end up in one of my Irish ancestors' villages, odds are they're speaking Gaelic, but can probably find an English speaker somewhere who might catch on that my dialect is very unusual, though unless I do something to tip my hand about my future knowledge, I still doubt they'd suspect time travel. Scientific knowledge could be written off in different ways, and I don't know enough 16th century history to really be able to say or do anything prophetic.

If my goal is to avoid being outed as a time traveler, I can probably play dumb well enough not to tip my hand. They might assume I'm an idiot, insane, a witch, a demon, a fairy, etc. but I can probably avoid being outed as a time traveler.

The future is harder, if time travel is a known technology/phenomenon, I imagine I'd be outted pretty quickly. If not, I suspect I'd probably be treated as insane or an amnesia patient or something, I can't think of any reason they would assume I'm a time traveler unless I make it a point to bring it up, maybe if they run some blood tests and notice I'm missing immunity to common future diseases or radioactive contamination from WWII or something. Even then they would probably assume I'm a descendant of a secret bunker cult or something along those lines that wouldn't break the laws of physics.