The first variant, with "people employed," sounds perfectly normal and natural to me. The second variant, with "employed people," sounds awkward.
I believe the reason that the second version sounds weird is that putting employed before the noun people emphasizes its adjective characteristics, while putting it after the noun emphasizes its verb characteristics (since ordinary adjectives don't usually go after the nouns they modify). Since the past participle "employed" is a non-finite form being used as an adjective, it has both verb and adjective characteristics, but depending on the usage, one 'side' can be emphasized over the other.
Compare the two sentences "Bob saw swimming fish" and "Bob saw fish swimming." The first sentence puts more emphasis on "fish" as what Bob saw, while the second places more emphasis on the action of swimming (what the fish are doing), even though in both cases "fish" is the direct object of "saw," and "swimming" modifies "fish."
For your example sentences, in the pre-nominal adjective position, the context might lead the reader to expect a word that describes a more fundamental or personal characteristic of the employees - like appearance or age. Example: "10 million red-haired people" or "10 million young people." You'd never say, "10 million people red-haired" or "10 million people young"! Just like in the "fish" example, you could replace "swimming fish" with "tropical fish", but not "fish swimming" with "fish tropical."
In your example sentences, "employed" isn't a fundamental or personal characteristic of "people" so much as a descriptor of their relationship to the industry. Employing the people is something the industry ("Manufacturing") does to them, so the word employed's passive verb side (the people are employed by Manufacturing) is emphasized over its adjective side. Thus, "employed" should come after "people" as in 1., not before it as in 2..
Another commenter has also observed that you could substitute the noun "employees" for either phrase. While I don't agree with ralph.m about both of your examples being "a tad awkward" (to me only the second one sounds awkward), this could be a regional difference. In US usage, I believe that your sentence 1. and ralph.m's version with 'employees' are equally valid and idiomatic, while sentence 2. is less preferable.
All 3 possibilities convey the same meaning; the only difference is style.