@essblack some questions to clarify what are you doing and be able to give you meaningful answers:

1) Did you installed the default collections?
2) If so, did you just re-use the default "Home" collection as the blog B you mention, or created a new collection for blog B? What type is it (http://b2evolution.net/man/collection-type-panel) ?
3) Can you share screenshots of blog B showing where are blog A posts being included?
4) Can you identify if it is a widget where mixed posts are displayed? If so, please share screenshot of that widget's configuration.

1.) No. I tried that the first go round and regretted it immediately -- it was just too much.

2.) I created a New Collection for what I am calling Blog B.

3.) Can't share screen shots at this time.

4.) Widget? I'm afraid you've got me there. I was not aware there was a widget involved in simple blog posts.

As an aside, I think B2Evo is working as advertised, but, unfortunately, after experimenting a little more with it yesterday afternoon, I think the answer to my question is no. Posts from collection A which are placed on the front page will by default show up on a new collection (collection B) if collection B also shares the front page style.

I may need a new domain, or at least a collection style which is not front page.

Thanks!

Everything is configurable.

There is absolutely no rule that forces posts from one collection to show up in another, or on the home page.

When posts form multiples collections show up in a single place it's often because there is an aggregation configured. You can change this here: http://b2evolution.net/man/collection-aggregation-settings