Your problem is the that $tmpline is a scalar with one value and you are then using it to find the single key '"data1", "data2", ... "data13"'. What you really want to do is the following

while ( $tmpline = <FROM> ) {
    chomp $tmpline;
    @data_from = split ';;', $tmpline;
    @from{@fields_from} = @data_from;
    while (($key, $value) = each %from) {
        print "$key => $value\n";
    }
}
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As an aside the substitution would have been better written as

$tmpline =~ s/;;/", "/g;
$tmpline = qq{"$tmpline"};
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