This will work under the assumption that all input files have the same number of lines. However, if you have for example

Sample of text-1.txt files:

Line_1:Line_1_1
Line_2:Line_2_2
Line_3:Line_3_3
Line_4:Line_4_4
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Sample of text-2.txt files:

Line_5:Line_5_5
Line_6:Line_6_6
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Sample of text-3.txt files:

Line_7:Line_7_7
Line_8:Line_8_8
Line_9:Line_9_9
Line_10:Line_10_10
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the array would have the content 'Line_9_9' and 'Line_10_10' in the second column (where one would expect content from the second file only). This is because push simply appends at the end of the array.

To avoid that it would be better to use fixed indexing instead of push:

So

my $i = 0;
while (<>) { # read from @ARGV
    chomp;
    push @{ $value[$i++] }, /:([^:]+)/; # get timestamp
    $i = 0 if eof;
}
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could be replaced by this

my $i = 0;
my $filecount = 0;
while (<>) { # read from @ARGV
    chomp;
    $value[$i++]->[$filecount] = /:([^:]+)/; # get timestamp
    if (eof) {
        $i = 0;
        ++$filecount;
    }
}
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This would put the timestamps always in the right places, but you would have to be prepared to have 'holes' in the array, if the input files have different number of lines.

You can test if an array cell has a value assigned with code like the following:

if (!exists $value[$line]->[$file]) {
  # no value assigned, there is a hole in the array
} else {
  # value assigned
}
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Hope this helps! Update: forgot a closing brace in the new code block. It is now fixed.