The author’s conclusion is about how one group will respond to self-deprecation (how employers will respond to employees). But the evidence is based on how a different group responds (how employees respond to managers).

This possibility wouldn’t hurt the argument, because the author is assuming that the self-deprecation caused managers to be viewed positively.

The author never assumes that self-deprecating humor is more effective than non-self-deprecating humor. As long as self-deprecation can help one be perceived more positively, the author’s argument can still work.

The author never assumes that nonhumorous self-deprecation wouldn’t be viewed positively. In fact, the author assumes that the self-deprecatory aspect of the managers’ behavior helps contribute to positive responses.

There’s nothing wrong with critiquing one part of advice, even if there are multiple parts. In addition, we can reasonably read the author’s critique as applying to both the “emphasizing one’s strengths” part and the “downplaying one’s weaknesses” part.