I took the freedom to slightly simplify your spec, using a lookup table. The output should be what I suppose you want, i.e. replace all occurrences of c1 etc. with c1 d1 etc.:

#!/usr/bin/perl
use strict;
use warnings;

my $fname_A     = "file_A.txt";
my $fname_B     = "file_B.txt";
my $fname_B_out = "file_B_out.txt";

my %subst;  # lookup table

open (my $data_fh, "<", $fname_A) or die "Couldn't open '$fname_A': $!
+";
while (<$data_fh>) {
    chomp;
    my ($find, $add) = (split /\t/)[2,3];
    $subst{$find} = $add;
    # print "$find => $add\n";  # debug
}

my $search = join "|", map quotemeta, keys %subst;

open (my $in_fh,  "<", $fname_B)     or die "Couldn't open '$fname_B':
+ $!";
open (my $out_fh, ">", $fname_B_out) or die "Couldn't open '$fname_B_o
+ut' for writing: $!";
while (my $line = <$in_fh>) {
    $line =~ s/($search)/$1 $subst{$1}/g;
    print $out_fh $line;
}
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The output might not be what you want in case the search strings aren't unique (because of the lookup hash), or if the substitutions aren't independent, such as when c1 => c2 in the first run through the file, c2 => d2 in the second run, etc. (because of doing it all in one go).