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Since "you receive exactly the number of visitors you purchase", you know it has to be fake. My suggestion would be to put this money into improving your website instead. They're not doing anything above board to generate actual traffic for you which means it's likely going to be bots or maybe some kind of traffic trading scheme (you visit websites in their list and those sites visit you) but I see no mention of that anywhere. It seems traffic does boost rankings but only for as long as that traffic remains and to be getting significant ranking improvements, a significant amount of traffic is needed from the examples I've seen in the past. As Cognitive SEO said, "impressions don't buy, real people do..." so I'd suggest thinking more about how you can rank higher and more about how you can deliver UX that leads to revenue. Here's Cognitive's article of their experience of picking up a large spike of real traffic from a Reddit thread - worth a read. As Marie Haynes pointed out in this Q&A thread on a similar topic, the key difference between buying traffic and generating traffic is that generating real traffic brings real user engagement and the potential for organic backlinks. These backlinks mean lasting results rather than a brief stint of improved rankings.

Thanks for your help, Bernadette. I really appreciate your advice. I had thought to crawl the site-- I see a few 302 redirects and one 404 response. Webmaster Tools does not indicate any errors found by Google. The link idea is a good idea-- when I took a look at our backlinks detected by OpenSite Explorer, I find that we have increased in the number of links in the last 3 months 120 (we had lost 50 links, but the domains linking to our site overlap completely). Moz does not show any of the links as spammy. Are there any other link-related tools that I should be considering here?