With a Custom HTML module, there is an Option and you can select Yes or No for Prepare Content. This is needed if you have something like the content plugin I developed to acknowledge this, as it does in Joomla Articles:
For example, there is a module mod_articles_latest, and I wish to add the Prepare Content option to this, so that when it is showing Joomla Articles it will process the above plugin example.
I found this link about Triggering Content Plugins, but I'm unsure if simply adding this code to mod_articles_latest, will make it work:
$text = JHtml::_('content.prepare', $text);