You're switching on ?x too late in the regular expression:

#!perl -w
use strict;
use Data::Dumper;
my $dat = "Just another cats meow";

sub print_matches {
    my( $re ) = @_;
    my @matches = $dat =~ /$re/;   
    print "Using $re\n";
    print "#matches=%s, matches=%s", scalar(@matches), Dumper \@matche
+s;
};

print_matches( qr{ (?x) (\w+) } ); 
print_matches( qr{(?x) (\w+) } ); 

__END__
Using (?^: (?x) (\w+) )
#matches=%s, matches=%s1$VAR1 = [
          'another'
        ];
Using (?^:(?x) (\w+) )
#matches=%s, matches=%s1$VAR1 = [
          'Just'
        ];
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The first whitespace is not governed by ?x.