Cannot understand result for multiline regex qr/( . $ .+ )/xms

For string "aa\nbb\ncc" I want to match from the last letter left to the first newline ("a") to the end of the multi line string and expected that

"aa\nbb\ncc" =~ qr/( . $ .+ )/xms matches a\nbb\ncc

and that

"aa\nbb\ncc\n" =~ qr/( . $ .+ )/xms matches a\nbb\ncc\n.

But I got no match for "aa\nbb\ncc" =~ qr/( . $ .+ )/xms and match c\n for "aa\nbb\ncc" =~ qr/( . $ .+ )/xms.

Using qr/( . $ ..+ )/xms I got the expected results (see example code).

Perl version 5.14.2.

Can anyone give an explanation for that behaviour?

perldoc perlre:

   m   Treat string as multiple lines.  That is, change "^" and "$" 
       from matching the start or end of the string to matching the start 
       or end of any line anywhere within the string.

   s   Treat string as single line. That is, change "." to match any character 
       whatsoever, even a newline, which normally it would not match.

       Used together, as "/ms", they let the "." match any character whatsoever, 
       while still allowing "^" and "$" to match, respectively, just after and 
       just before ewlines within the string.

   \z  Match only at end of string

Running the following example code :

#!/usr/bin/env perl

use strict;
use warnings;

print "Multiline string : ", '"aa\nbb\ncc"', "\n\n";
my $str = "aa\nbb\ncc";

print_match($str, qr/( . $ )/xms);       # matches "a"
print_match($str, qr/( . $ . )/xms);     # matches "a\n"
print_match($str, qr/( . $ .. )/xms);    # matches "a\nb"
print_match($str, qr/( . $ ..+ )/xms);   # matches "a\nbb\ncc"
print_match($str, qr/( . $ .+ )/xms);    # NO MATCH ! Why ???
print_match($str, qr/( . $ .+ \z )/xms); # NO MATCH ! Why ???

print "\nMultiline string now with terminating newline : ", '"aa\nbb\ncc\n"', "\n\n";
$str = "aa\nbb\ncc\n";

print_match($str,