Took a moment to take care of it. Here's the PR, and my repo (PR was approved, use the original repo link instead. I assume a new CPAN release is imminent) that you can clone from (git clone https://github.com/ronsavage/Tree), then checkout the "remove_fatal_warnings" branch (git checkout remove_fatal_warnings), then install as normal:

perl Makefile.PL
make
make test
make install
[download]

Output after installing the changes:

Deep recursion on subroutine "Tree::_fix_height" at /home/spek/perl5/p
+erlbrew/perls/perl-5.26.1/lib/site_perl/5.26.1/Tree.pm line 333.
Deep recursion on subroutine "Tree::_fix_width" at /home/spek/perl5/pe
+rlbrew/perls/perl-5.26.1/lib/site_perl/5.26.1/Tree.pm line 346.
Deep recursion on subroutine "Tree::event" at /home/spek/perl5/perlbre
+w/perls/perl-5.26.1/lib/site_perl/5.26.1/Tree.pm line 198.
success
[download]

Update: I just added a quick and dirty test file to the PR to ensure the new functionality Does The Right Thing. I do that normally in the process of creating a PR, but I had urgent business to tend to earlier and figured the test could wait a bit. Note: I used the exact code OP specified to demonstrate the problem.