"Push" seems like a poor name for this. It doesn't imply anything other than calling the template from perl code, i.e. the same thing I referred to as "pipeline."
The trick is to look at it from the capabilities of the template
not how the template is called. the definitions
of push and pull-style rely on what the template can do, not how the template is called.
I also wouldn't lump HTML::Seamstress and XMLC in with Template::Recall and StringTemplate.
From the standpoint of template capabilities given in the definition, you can see why they would be lumped together. However,