I'm not sure what exactly is the problem, but the background colour seems to work if I change -selectbackground to plain -background.

Trying to configure -selectbackground without style leads to

Tk::Error: unknown option "-selectbackground" at /usr/lib/perl5/vendor
+_perl/5.14/x86_64-cygwin-threads/Tk.pm line 251.
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which seems to indicate you can't change the option for a single entry.

Also, remove the declaration of $tree_element and declare it inside the sub:

sub abba_browse {
    my $tree_element = $tree->info('selection')->[0];
    # ...
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