I'm not sure this actually refutes a relationship between offshoring and manufacturing employment. It's possible it's purely a result of automation getting better, and would have happened identically with no major shifts of trade. But given that the increase in offshoring makes labor-intensive industries much cheaper to locate elsewhere, it's also possible that market forces have accelerated the U.S.'s shift to less-labor-intensive industries. That is, we haven't just automated existing industries as technology has gotten better, but have actively stopped manufacturing certain things that are hard to automate, even though there's still demand for them, because we can't compete with cheap labor. We then put our resources into manufacturing easier-to-automate things instead, which keeps total output high.
If you break down the total manufacturing data and look at labor-intensive sub-sectors, you don't see the same upward trend in output. US textile manufacturing, for example, has totally collapsed, not just in employment but also in output.