I've spent 2 days researching and reading about ClickOnce deploy and tried and tried to get it to download updates without much luck. Found the answer:

You must set the Min Version and Check updates before startup from the very first version. Otherwise the initial version will get around to downloading it whenever it feels like it.

So this initial version has the Min Version specified and the following tag in it.

<!-- When to check for updates -->
<subscription>
<update>
<beforeApplicationStartup />
</update>
</subscription>