My guess: the entire right hand expression is evaluated before assignments are made.

Of course it does, but it doesn't explain anything. The question can be phrased as "Why is the output of the first snippet different from the output of the following snippets in the following code?"

$ perl -E'$i=0; ($j, $k) = (++$i,   ++$i);   say "j:$j k:$k";'
j:2 k:2

$ perl -E'$i=1; ($j, $k) = ($i++,   $i++);   say "j:$j k:$k";'
j:1 k:2

$ perl -E'$i=0; ($j, $k) = (++$i+0, ++$i+0); say "j:$j k:$k";'
j:1 k:2
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The answer is here.