You are correct - the capturing parens are not necessary,
In that case, the originally posted code is correct:

        # Split on multiple spaces using regex captured matches
        my @temp_and_starts = $_                              =~ /[^\s
+]+/g;
        my @last_AT_fracs   = <$in>                           =~ /[^\s
+]+/g;
        my @twenty_SFs      = (<$in> . <$in> . <$in> . <$in>) =~ /[^\s
+]+/g;
[download]

and my test below shows that it works:

$ perl -E '$_="This and that and other";@x=  $_=~ /[^\s]+/g;; say for 
+@x'
This
and
that
and
other
[download]