Your use of Data::Dumper to dump the data you're working with is helpful to us. It proves once and for all that the data you're dealing with isn't valid JSON.

use strict;
use warnings;
use Data::Dumper;
use File::Slurp;
use JSON::Tiny;
use feature qw/say/;

my $json = read_file(\*DATA);

my $j = JSON::Tiny->new;

my $decoded = $j->decode($json);

if( defined $decoded ) {
  say Dumper $decoded;
}
else {
  say $j->error;
}

__DATA__
{
  "alertCounts" : [
    {
      "count" : 5,
      "rule" : "rule1"
    },
    {
      "count" : 16,
      "rule" : "rule2"
    }  
  ],
  "balArray" : [
    {
       "containerArray" : [],
       "name" : "user_ip"
    },
    {
      "containerArray" : [
        {
          "entryArray" : [
            {
              "action" : "flag",
              "expires" : "00:00:00",
              "hitsSinceAdded" : 56,
              "name" : "/my/page",
              "priority" : 4,
              "rule" : "rule1",
              "timestamp" : "15:28:40.150"
             }
           ],
          "name" : "192.168.1.100"
        },
        {
          "entryArray" : [
            {
              "action" : "flag",
              "expires" : "00:00:00",
              "hitsSinceAdded" : 185,
              "name" : "/my/page",
              "priority" : 4,
              "rule" : "rule2",
              "timestamp" : "15:12:55.961"
            }
          ],
          "name" : "192.168.1.101"
        }
[download]

...and the output...

Malformed JSON: Expected comma or right square bracket while parsing a
+rray before end of data
[download]

Or once again, since you're using JSON:

, or ] expected while parsing array, at character offset 1004 (before 
+"(end of string)") at ./mytest.pl line 13.
[download]

If you have valid JSON, post your valid JSON. If you have invalid JSON, don't expect code that parses JSON to work.