Is there any problem with tweeting at a time when it is Shabbos somewhere in the world? Jewish followers may reply or re tweet etc.
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I'd seen the question asked years ago about someone in Israel, after shabbos had ended, doing online transactions (including making an ATM withdrawal) that will affect a US computer while it's still shabbos there. The response was that if everything's automated, it's permissible.
(This is related to a debate between the academies of Hillel and Shammai in the mishna -- I'm allowed to leave my candles burning on shabbos, as it's not my concern whether my inanimate objects rest on shabbos.)
The trickier question becomes if you think your tweeting will cause others to break shabbos. I guess that depends who your followers are. Maybe limit your Friday-afternoon tweets to really boring stuff? :)
Closely related: must you shut down your blog before shabbos?