When you publish an entry template in a blog it automatically runs the main index and archive index templates. It also updates any category pages in the blog. I don't see that happening to the parent website index template, so you have to do that by hand.
[Update] I have abandoned the complex Movable Type index page in favor of a page that is entirley contained in a copy of the main index page I cloned. It does not call ny header or footer modules, or the insanely complex Entry Summary module. The page calls a local stylesheet that is linked to itself so I can modify it with Stylizer and have MT save the changed file instead of overwrite it. The page is 8 boxes that have the main subjects as title. I call out the appropriate entries with a tag array like:
<li><a href="<$mt:EntryPermalink$>" target="_blank"><$mt:EntryTitle$></a></li>
This creates a list of entries that link to the perma-link for the entry.