Rated 3 out of 5 stars
Is it possible to reuse the original open action? This way, 'Tree style tabs' might be able to track it as a child tab, may be you should install 'Tree style tabs'(it is really a great plugin which improves productivity), and do some tests.This review is for a previous version of the add-on (22.214.171.124-signed.1-signed). This user has other reviews of this add-on.
What original action? In any case, wouldn't it make more sense to tell the 'Tree style tabs' author to fix his extension rather than everyone else making workarounds for it? :-)
Btw, there is a Support Site for these kind of discussions.