Strictures are your friend (use strict; use warnings; - see The strictures, according to Seuss). In this case forcing you to declare variables with my may have made you think about the scope of $u_set and that may have led you to realize that the print is in the wrong place, and that may have led you to realize that the for loop was only performing one iteration, and that may have led you to notice that you used a tab character to split on instead of a comma. A better version of the code might look like:

use strict;
use warnings;
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);

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

    print "Union of strings: $u_set\n";
}
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Note the Perlish for loop and avoidance of object indirect calling of the Set::IntSpan constructor.