Is there a special word for someone who got transported to another world/time/universe?

Time traveller? (It does not have to connote willingness, or an ability to travel at will.)

A phrase I know of is - "spirited away"

Wikipedia uses the term "fish-out-of-water" in the context of discussing the Russian word:

In science fiction, with communist censorship gone, many various portrayals of future appeared, including dystopias. Post-apocalyptic fiction, time travel and alternate history are among the most popular genres, represented by authors like Vyacheslav Rybakov, Yuri Nikitin, among many others. Overuse of fish-out-of-water plots for time travel and parallel worlds led Russian SF&F journalists to coin the ironic slur popadanets (Rus. попаданец, lit. getter) for such characters. [bolding not in original]

(Russian science fiction and fantasy)

A "fish out of water" is a general English idiom for someone who feels out of place or uncomfortable in their environment (not just time travelers or people in parallel universes).

The website TV Tropes (a wiki that lists "tropes" used in literature and other media) describes the time-travel situation specifically with the term "Fish Out of Temporal Water." I haven't heard this exact term used in conversation, but it is an understandable way of making the general idiom more specific.