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.
TLDR: When you paraphrase someone, you should cite them.
I agree with the spirit of the answer by @Kimball, but I come to a different conclusion based on the specifics of your case. You say:
I reworded parts of his sentences
If you take someone else's writing and paraphrase it, you should probably be citing them. Otherwise you risk committing what Harvard's Honor Council calls uncited paraphrase, which is a form of plagiarism:
The rule of thumb here is simple: Whenever you use ideas that you did not think up yourself, you need to give credit to the source in which you found them, whether you quote directly from that material or provide a responsible paraphrase. (Harvard Honor Council: What Constitutes Plagiarism)
If you had simply read the same works and happened by chance to write a similar summary of them, then you would not need to cite the other author. But if you read the other author's summary and then paraphrased them, as your question seems to state, then you are relying on their work and should cite them.
Note: If you meant that your sentences could merely be interpreted as re-wording the other author's writing, but that you wrote them before you read the other version, then @Kimball's answer applies (though you may still wish to cite the other author for the sake of completeness). If that's the situation, then it might be helpful to re-word your question to make this clear.