There are a few changes I'd like to suggest (such as breaking this code up into functions), but answering your immediate problem, I would create a hash with each key named with a csid. Then every time you process a line, you can increment the hash entry that matches the csid. You'll end up with the hash having a unique count for each file. To create the hash, you can do this:

my %line_count;
for my $csid (@csid_list) {
    $line_count{$csid} = 0;
}
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Then, just before you use the counter variable in your print statement, you can do this:

++$line_count{$csid};
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This will allow you to keep count on each file, even if the csids in the source file are not in sequence.