You can install a gnu version of tee.exe on your Windows machine or just use your own tee. You like tee, so just use tee.

Update: I tried using tee command here too but didnt work - the below works on my Windows machine.
tee.pl

#!usr/bin/perl -w
use strict;
$|=1;  #turn autoflush on

sub usage () 
{
   print "TEE USAGE:\n".
         " program | tee outfile\n".
         " sends stdout from program to outfile\n";
         exit;
}

my $filename = shift @ARGV;
usage unless $filename;

open (OUTFILE, ">", "$filename")
          or (die "Can't open OUTFILE: $!");

while (<>)
{
  print;
  print OUTFILE;
}
[download]

Update: In your program, unbuffer stdout. There is no need for the eval. There can be issues about how to run a perl program on Windows without having to say "perl" explictly - but that's a different subject (and this is possible to do).

#!/usr/bin/perl -w
use strict;
$|=1;  #unbuffer stdout

print "File split start time is ", scalar localtime();
[download]

prints:
C:\TEMP>perl test.pl | perl tee.pl xxxxx
File split start time is Fri Mar 30 05:57:41 2012
C:\TEMP>type xxxxx
File split start time is Fri Mar 30 05:57:41 2012
C:\TEMP>
[download]