I'm not sure if it's common for publishers to use anti-plagiarism software, as I'm not a publisher, so perhaps a user who is more familiar with the publishing process can give a more direct answer. However, since you're worried about plagiarism in your work, I'll offer advice on what to look out for and how to cite/paraphrase appropriately.
You definitely have to be aware of what is and is not plagiarism when it comes to paraphrasing, quoting and referencing other material in nonfiction works. It surprises people to learn, for example, that "paraphrasing" can still be seen as plagiarism if it's too close to the original work, even if you didn't use the exact words or phrases in the work. So my advice would be:
Remix and change, don't just rephrase.
Be careful that you are truly, completely rephrasing and remixing the work you're referencing, and not closely copying its words, ideas or style. Plagiarism is not just using the same words; plagiarism can also be found in recycling the order of ideas in a work, or resembling the work it comes from despite using different language and phrasing.
For reference, see the scandal in which Filip Miucin, an IGN editor, was found to have been closely copying the ideas and order of many small reviewers, even though he didn't technically use their exact words. The similarity between the reviews, and the way in which he copied their flow of ideas and order of ideas, was enough. (Source) (Source)
Cite, cite, cite!
Whenever you look at another work for reference, cite it. When it gives you an idea, cite it. Cite, cite, cite as much as you can, even if you feel like it's unnecessary or excessive, because it is always better to reference too much as opposed to not referencing enough. Even if you have a sentence that starts like this:
The idea of this unique interspecies relationship is explained in Birds of North America by the Cornell Lab of Ornithology, where...
It's always important to give proper credit if you got an idea from somebody else, no matter how small, and it feels less like you're "stealing" somebody's ideas if you explain where you got them from and why they're useful to mention in your work. And it probably makes somebody happy to see that their work inspired and helped yours, which is an additional bonus!
Keep in mind the legal definition of plagiarism, and that nonfiction is treated differently from fiction.
Plagiarism in fiction, as defined in the United States legal system by court proceedings like this one, is that first of all, copyright infringement can occur even if exact lines are not literally copied, (Source) and second, that the nature of the copyrighted work and the derivative work is important to the discussion. You have much more leeway when writing nonfiction because you are writing informative, factual literature. (Disclaimer: I'm not a lawyer and state laws may vary.)
In conclusion? I wouldn't worry about it and you are probably fine. Just make sure to keep these things in mind going forward.