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";
}

...
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