When and how did journal publications start to have such an important role in evaluating researchers?
Widespread peer review in journals is a relatively recent phenomenon. Famously, Einstein and Rosen wrote an incorrect paper arguing that gravitational waves don't exist, which was rejected by a reviewer for Physical Review. The rejection made Einstein angry, and he wrote:

Dear Sir,
We (Mr. Rosen and I) had sent you our manuscript for publication and had not authorized you to show it to specialists before it is printed. I see no reason to address the—in any case erroneous—comments of your anonymous expert. On the basis of this incident I prefer to publish the paper elsewhere.
Respectfully,
P.S. Mr. Rosen, who has left for the Soviet Union, has authorized me to represent him in this matter.

This was in 1936, and Einstein had already published many papers by that point. It appears from his response that peer review was not yet common at that time.
(Source: &quot;Einstein versus the Physical Review&quot; in Physics Today.)
Googling this I stumbled across a blog post by Michael Nielsen who links to some historical papers on the growth of peer review that may interest you.