How did the refereeing system of Gösta Mittag-Leffler's Acta Mathematica function from 1882 to (about) 1918?

(Not an answer, too long for a comment.)

Is it even clear that there was a refereeing system in place? As opposed to, say, the editors looking through each submission and giving a thumbs up/thumbs down.

There is an interesting story about a 1936 paper of Einstein and Rosen on gravitational waves, which suggests that even that recently, peer review worked very differently. Einstein and Rosen had discovered an erroneous argument proving mathematically that gravitational waves couldn't possibly exist, and they submitted it to Physical Review. The handling editor, John Tate Sr., had usually accepted Einstein's papers without any refereeing process, but felt skeptical about the result. So he sent it to Howard P. Robertson for review, who wrote a ten-page report explaining why the argument didn't hold water. Einstein was not happy about this, and wrote the following letter in response:

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.

Einstein never again published in Physical Review.

Looking over the following references, I believe that they contain some of what is being asked after:

Nickerson, Sylvia (2012). Referees, publisher’s readers and the image of mathematics in nineteenth century England. Publishing History, 71, 27-67. Link.

(Sample quotation: "The article examines the processes of refereeing, and the role of the editor, at nineteenth century mathematical journals by looking at the Cambridge Mathematical Journal and Acta Mathematica," p. 27.)

One of the references in the above manuscript is Chapter 8 (pp. 139-164) in an earlier work:

Parshall, K. H. (2002). Mathematics Unbound: The evolution of an international mathematical research community, 1800-1945 (No. 23). American Mathematical Society. Chicago. Link.

(Chapter 8 is entitled: "Gosta Mittag-Leffler and the Foundation and Administration of Acta Mathematica.")

And among the many references in this latter chapter is the following article of potential interest:

Domar, Y. (1982). On the foundation of Acta Mathematica. Acta mathematica, 148(1), 3-8. Chicago. Link.