I'd recommend
Time::Duration and
Time::Duration::Parse for this to save effort, assuming you can get it to give you the right output (for example, it interprets strings in the form 'dd:dd' as hh:mm instead of mm:ss, but you can add ':00' to the end to fix that).
Also, I'd probably write the main logic differently:
my $timespec = qr/\d{2}:\d{2}:\d{2},\d+/;
my ($infile, $offset) = @ARGV;
usage() unless defined $offset and $offset =~ /^[+-]?\d+$/; # integer
...
if (my ($start, $end) = /^($timespec)\s-->\s($timespec)/) {
$_ = time_to_sec($_) += $offset for $start, $end;
print "$start --> $end\r\n";
}
...