With supertab you can press whatever your next keystroke would be instead of enter (i.e. a period to call a method after tab completing an object). I’m not sure you can mimic the Sublime functionality exactly.
The best content I’ve seen about Vim’s completion is the talk talk Let Vim Do the Typing by thoughtbot’s very own @georgebrock. It does a great job describing the various completion modes and sources Vim can pull from.