Is paraphrasing Jack's sentence considered plagiarism, given I cite the original author Z?
Plagiarism is the act of passing off another work/writing as your own.  

If I read the question right, you are saying something like the following:  you wrote a background section about about works [1], [2] and [3].  Jack also independently and prior to you wrote a summary about works [1], [2] and [3].  And some of your sentences happen to be similar.  This is not plagiarism.  This is normal, because you're talking about the same things, and because both of your descriptions are influenced by the original sources [1], [2] and [3].

What would be plagiarism is if you were to copy large chunks of text into your paper without marking it off as a quotation.  In my field (pure math) it's common that different papers have whole sentences which are virtually identical.  (There must be hundreds of papers with the sentence "Let G be a group.")

I also don't think it's necessarily necessary to cite Jack's work just to say they summarize [1], [2] and [3] also.  If you think looking at Jack's presentation also will help the reader, or you used aspects of Jack's presentation, then you should cite Jack.