Is paraphrasing Jack's sentence considered plagiarism, given I cite the original author Z? I have a specific question. I am working on my academic paper.

I came across this unpublished paper online written by a PhD student. Although, his topic is different, some parts of his paper relates to the background section of mine. For my background section, I am using three different books as source material. This person, let's call him Jack, has also used the same books. 


  Question: If my sentences are similar to Jack's (i.e. I reworded parts of his sentences) is it considered plagiarism, given, I cite the original source (that we both used): the books? 


Example (made up): 


Jack: According to Greene (2001), the program was implemented in 1991 to ensure a more efficient organization of the workers and, subsequently, to facilitate their unionization.
Me: The Unity program was created in 1991 to efficiently organize the labour force and, subsequently, to help workers join the labour union (Greene, 2001)


Some terms are hard to replace with alternatives without fully changing the meaning or using too many words. 

I have read the book, the main source material, and have cited it in my sentence. But, my sentence is very similar to Jack's. Would this be considered plagiarism even though the idea is not Jack's? 

I have no problem referencing Jack's paper in my Reference section at the end, but I don't want to use intext citation citing Jack's paper.
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.