How to make a custom block listen to context module?
Firstly, You can try putting a regular block at a regular region created by drupal core in context. That should work.

Then compare the different results you got for your custom block and custom region. Try putting your custom block at regular region, or putting regular block at your custom region.

Also, You may need to double check the 'custom region' you mentioned at question does exist at page.tpl.php. I.e the code does print the 'custom region' in page template, like

&lt;?php print render($page['your_custom_reagion']); ?&gt;