Textmate, the original, used onigurama for regular expressions.
E and Sublime, seek to ensure compatibility with textmate grammars.
I'm pretty sure I've read sublime uses Boost regexes, it uses Boost in a lot of places actually.
As far as compatibility, a) it's the perl variant, not posix variant. b) i'd check the textmate manual. Sublime tries to ensure compatibility with Textmate, and textmate right now has better documentation, so look there for the syntax you can use.