Text you put in MediaWiki:Growth-homepage-banner is parsed like normal wikitext, and then displayed on Special:Homepage. However, the text is not wrapped in <div class="mw-parser-output"></div>, and this means that any templatestyles that are included won't apply (because all rules in templatestyles' output are prepended with .mw-parser-output).

To replicate:

Put this in [[MediaWiki:Growth-homepage-banner]]:
{{some template}}

Put this in [[Template:Some template]]:

<templatestyles src="Some template/styles.css" />
<span class="colorless-idea">Sleeping furiously</span>

Put this in [[Template:Some template/styles.css]]:

.colorless-idea {
  color: green;
}

Observe the output in [[Special:Homepage]].