HTML::Parser is not to blame. You have logic errors.

First #$parser->report_tags( qw( @report_tags ) ); should be #$parser->report_tags( @report_tags );.

Second, your text_handler is flawed. You test     if ( $self->{_stack}->[0] ) { # filters out text outside a tag. which will FAIL every time since '<@report_tags>' and/or '</@report_tags>' are never encountered. The same would happen if you only had text as input. I suggest you rework your text_handler, and in the future always start with a small example which demonstrates the problem (it's easier to diagnose the actual problem that way).