It looks like your strings are comma-separated, but you are splitting them on tabs. You are also overwriting $u_set each time round the loop, so you'll need to accumulate the result differently.

I'd probably aim to write it something like this:

use strict;    # always
use warnings;  # always
use Set::IntSpan;

my $TM_part1 = "25-40,74-93,95-120,130-149";
my $TM_part2 = "31-47,84-99,107-123,137-151";

my @split_TM1 = split ',', $TM_part1;
my @split_TM2 = split ',', $TM_part2;

my $u_set = join ',', map {
  my $set1 = Set::IntSpan->new($split_TM1[$_]);
  my $set2 = Set::IntSpan->new($split_TM2[$_]);
  intersect $set1 $set2;
} 0 .. $#split_TM1;

print "Union of strings: $u_set\n";
[download]

.. but if you're not comfortable with map, you can accumulate the results in an array instead:

use strict;    # always
use warnings;  # always
use Set::IntSpan;

my $TM_part1 = "25-40,74-93,95-120,130-149";
my $TM_part2 = "31-47,84-99,107-123,137-151";

my @split_TM1 = split ',', $TM_part1;
my @split_TM2 = split ',', $TM_part2;

my @u_set;
for my $i (0 .. $#split_TM1) {
  my $set1 = Set::IntSpan->new($split_TM1[$i]);
  my $set2 = Set::IntSpan->new($split_TM2[$i]);
  push @u_set, intersect $set1 $set2;
}

my $u_set = join ',', @u_set;
print "Union of strings: $u_set\n";
[download]