This time travel fad actually started in novels.
I believe the first novel in this genre that hit it big was 《寻秦记》 （Looking for the Qing Dynasty) by 黄易. (It was later adapted into a popular TV series.) It's about a special ops guy who travelled back in time and found his fame and fortune fighting for the future first emperor of China. A host of copy-cat works followed, and because the male protagonist usually boasts numerous romantic exploits, this type of character is nicknamed the 'stallion'.
What followed was very interesting. (Mostly young) woman novelists noticed this and said to themselves 'Surely we can do wish-fulfillment too.' and started sending girls back into history.
A typical female time-traveller, (穿越女), with her knowledge of modern medicine, business acumen, pop songs, makeup mastery and high EQ (emotional quotient) in general, always proves to be very successful in her romantic conquests, sometimes holding several princes in her thrall at once. In short, she's Mary Sue's Chinese soul mate.
Her success definitely speaks to female empowerment. (In one memorable episode in one particular book, the female protagonist manages to perform amputation surgery on her lover with only her memory of a medical text book she once translated to aid her. Even Claire from the Outlander series would boggle at this achievement, I declare.) But because her success is always mainly on romantic terms, she probably won't win any feminist award anytime soon... However, that's an issue all romance writers have to deal with.
As a plot devise, time travel is very clever. It allows the author to retain his or her modern sensibilities (as these novels are largely told in the first person voice,) and creates instant intrigue (how will she blend in?). Whatever the historical backdrop, it is always a nice change of pace for the mostly urban and web-savvy readers of these novels. (To be fair, some of these authors, though firmly in the minority, do care about historical verisimilitude. At their best, they do what HBO's 'Rome' does to Roman history.)
Different from their western counterparts is the time-travel mechanism used by these Chinese authors. By and large it's done through backward reincarnation -- the traveller unknowingly enters into a new body rather than coming with her modern person. My guess is that this choice is mainly economic, since the new body usually comes with a wealthy upper class family and a girl servant or two. Another side benefit is that the new body is usually younger (and of at least presentable looks). Since the time-traveller is usually college educated, that would put her towards the tail end of marriageable age in the old times, which clearly won't do. I also have to suspect that this caters to our culture obsession with youthful beauty.
This plot also gets very old very fast. For instance, the consequence of having a passive adventurer is that the first few chapters always need to deal with the time-traveller's sense of dislocation and their grief over the loss of their previous life. (Very few get to ever travel back!) Many novels only pay lip-service to this aspect, and I can hardly blame them, but that always sets the wrong tone for the rest of the book. Some writers however manage to play up all these cliches for great comedic effect.
By far the most popular destination is the Qing （清） dynasty. About a decade ago, TV palace dramas set in that period became hugely popular, and a lot of these writers grew up watching them, so this is definitely the historical period they and their readers are most familiar with. I personally am not a fan however, since I always have trouble keeping track of the cast of royal half-brothers/a.k.a. romantic interests whose names are very similar and who are often referred to only by their birth order, most commonly going up to fourteen.
(I recall only one instance where the protagonist goes outside China -- to ancient Greece, and that was a fantastic read. As with all genre fiction, the seasoned reader gets the fun of seeing how well the writer manages to wrestle with all the conventions in her chosen genre. 不破不立～～)
The closest counterpart to Chinese time-travel romance in Western romance literature is perhaps paranormal romance. Both are fantasy, but given a chance to fantasize, somehow we usually prefer to escape back into our past instead of acquiring superman abilities.
(Now only if there were a mefi FPP that gives me a chance to write up my experience with 网文 in general...)
P.S. 疏忽了。。。 I forgot that in a book I didn't finish, there's a girl who managed to travel into Pride & Prejudice and became an independently wealthy Lydia.