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Toolbars not displayed when opening a Frameset in a Composite Application for the Lotus Notes Client

Here is an oddity we have run in to when developing a Composite Application design for the Lotus Notes Client:
The Notes client is configured to display the Mobile Toolbar (File->Preferences->Toolbar->Toolbars - checkmark in Mobile).
Then I open up the Composite Application.
I see the Mobile Toolbar just fine:

Then I switch to a different page in the Composite Application, and the Tollbar disappears:

The Page I switch to has just one Component which opens up a Notes URL for a frameset sitting in the same database:

It loks like the Notes client does not detect that I am inside a Notes Database.
This is in a Notes 8.5.2 client. Composite Application Design is a pain.