Does the word "efficient" usually refer to polynomial time or polylogarithmic time?
There is no one true answer.  It depends on context.  The most common context is one where polynomial-time is taken as more or less synonymous with efficient, so if you had no further context, I would certainly guess "polynomial time".  Polylogarithmic time is used only in very narrow contexts.

In general, if you think your audience might not be sure about the meaning, then I recommend you to define your terms.