%construct and %TEST are identical at the end of this code, is that what you want? I think the first part of your code could be simplified like this:

my %construct;
push @{ $construct{$_->[1]} }, $_->[2]
    for (@records);
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(where @records is some collection of array refs like you have in your first line of code). Just push onto the appropriate array as you see each item. Having a two-layered hash seems redundant. Your while loop is simply making a copy of the data in %TEST, and doesn't seem to be doing anything to the data.

How can I perform work on each of the values (i.e. maybe a join) and then print the key with its corresponding list of values?

I'm not sure I really understand your question. To get back to your data to perform some work on it, you can use the while loop you already have (using $key and @values). I don't know what you mean by "maybe a join" -- since all the arrays are indexed by different keys. Perhaps an example data set would help. To just print the key with its associated list of values:

while (my ($k,$v) = each %construct) {
    print "$k has values: " . join(',', @$v) . "\n";
}
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blokhead