The greediness is just your first problem.

Problem #2: You're using the g modifier in list context, causing all the matches to be returned at once. You'll never print anything other than the first file name.

pos $data = 0;
my $len = length $data;
while (pos $data < $len) {
   if ( $data =~ m{ \G ( .+?  \. xml ) }gcxms ) {
      print "$1\n";
   }
}
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Problem #3: If there's anything after the last .xml, you have yourself an infinite loop. Checking if pos is less then length is a bad idea when using the c modifier. Fix:

pos $data = 0;
for (;;) {
   $data =~ m{ \G ( .+?  \. xml ) }gcxms
      or last;

   print "$1\n";
}
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Finally: Using the c modifier is rather useless, ugly if you only have one regexp, and it's rather complex (as shown by the number of errors). Fix:

while ( $data =~ m{ \G ( .+?  \. xml ) }gxms ) {
   print "$1\n";
}
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Tip: If you really did have a use for c (e.g. if you were writting a lexer), then you'd have multiple regexps, and aliasing $_ to the variable containing the text would be worthwhile.

for ($data) {
   pos() = 0

   for (;;) {
      /\G ... /xgc && do { ...; next };
      /\G ... /xgc && do { ...; next };
      /\G ... /xgc && do { ...; next };
      last;
}
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