Is it possible to apply a block to a page template and then use "Setup on Child Pages" on the block to apply it ONLY to pages using that specific page template?

From my experimentation, it seems that if I add a block to a page template (via Pages & Themes -> Page Types -> {name} -> Output, then Edit for a specific template) it will apply that block to ALL pages using the page type, rather than applying it to the specific page template where I added it.

Hope that makes sense.