Why is my custom block template applying to all blocks?
As stated in Drupal 7 Template (Theme Hook) Suggestions, it suggests the file name structure to be like block--sidebar_first.tpl.php.

==EDITED==

In my themename.info file I declared

regions[sidebar_first] = First Sidebar


Copied the core block.tpl.php file, renamed it to block--sidebar_first.tpl.php, added "BLOCK NAKO" text.

Then I Flushed Caches. The image below is the result.



As you can see the footer region blocks doesn't have the override that I only set for blocks within the sidebar first region.