Your problem description is incomplete insofar as you do not show us test_if_txt_box_contents_passed_back or updt. See How do I post a question effectively?. In particular, creating a self-contained example would be illuminative.

My guess would be that the $self variable you are calling update on in your sub is a different variable than the $self object that contains contents. Think about it this way:

$main_self->{txt_box}=txt_box->new( $main_self->{frm}, sub {$main_self
+->updt} );

...

sub new {  my $class = shift;  my $new_self = {}; bless( $new_self, $c
+lass ); #std line
    $new_self->{parent_widg}=shift;
    $new_self->{sub_to_call_on_keypress}=shift;   <===================
+LOOK HERE
    $new_self->{contents}='';
    $new_self->{entry}=$new_self->{parent_widg}->new_ttk__entry( -widt
+h => 50, -textvariable => \$new_self->{contents}, );
    $new_self->{entry}->g_pack( -expand => 0, -fill => 'x',  -side => 
+top);   #-fill => 'both'
    globals::new_bindtag('new_tag',$new_self->{entry},4); 
    Tkx::bind( 'new_tag', "<Key>", [ sub { $new_self->upon_keypress(@_
+) }, Tkx::Ev("%W","%K","%k") ] );
    return $new_self;  } #std line

sub upon_keypress { #calls the sub/method you supplied...if an ordinar
+y sub you supply \&sub_nm if method then just obj->method_nm
    my ($new_self, $win, $key_nm, $key_no) = @_; #tick
    print "in upon_keypress and so far you've got $new_self->{contents
+}\n "; #tick
    $new_self->{sub_to_call_on_keypress}->( $new_self->{contents}  ); 
+#bug here...$self->{contents} gets passed to ORDINARY SUB but not upd
+t method    <===================LOOK HERE
}
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Your keypress routine uses $main_self in what is passed, not $new_self that has the contents field.