[jackie_w]

The current problem is that, in the Viewer, each TOC "Part" is pointing to the wrong place. Each "Part" should be pointing to the same place that the first "Chapter" following the "Part" points i.e.
Part 1 to Chapter 1
Part 2 to Chapter 3
Part 3 to Chapter 4
Part 4 to Chapter 8
Part 5 to Chapter 13
So we need to use Calibre Tweak-epub to tweak toc.ncx, in your text editor, so that it does.

Here is the relevant section for "Part 1" in the toc.ncx in my version of the epub:

    <navPoint id="e2c7f948-bfe9-41ab-96e3-b664d1569949" playOrder="2">
      <navLabel>
        <text>Part 1 ~ Earth Time</text>
      </navLabel>
      <content src="SMem2utf8_split_002.htm#calibre_toc_2"/>
    </navPoint>
    <navPoint id="7ee7a724-dd85-4146-951f-235ca86c50da" playOrder="3">
      <navLabel>
        <text>Chapter 1: The Awakening</text>
      </navLabel>
      <content src="SMem2utf8_split_003.htm"/>
      <navPoint id="20319fe0-acfe-49bb-9a46-53231822216a" playOrder="4">
        <navLabel>
          <text>A Gift for Someone…</text>
        </navLabel>
        <content src="SMem2utf8_split_003.htm#calibre_toc_30"/>
      </navPoint>

What you need to do to correct "Part 1" is to change the red bit to match the blue bit.

... and similarly for "Part 2":

    <navPoint id="db1618d1-bc2e-412c-ac9e-e5e99bc7dbd8" playOrder="21">
      <navLabel>
        <text>Part 2 ~ Day One</text>
      </navLabel>
      <content src="SMem2utf8_split_004.htm#calibre_toc_5"/>
    </navPoint>
    <navPoint id="1cb9e2c9-392e-46df-aa07-d370c3e7ecf7" playOrder="22">
      <navLabel>
        <text>Chapter 3: The Prophecy</text>
      </navLabel>
      <content src="SMem2utf8_split_005.htm"/>

Then repeat for Parts 3, 4 and 5.

When you've finished, save toc.ncx.
Close the text editor.
Close the file browser window (listing all the files inside the epub).
Click on "Rebuild epub".
View epub in Calibre Viewer and click on each "Part" in the TOC to make sure it now points to the right place.
...and that should be it...

By the way I've opened a new ticket in Calibre Bugs. If the powers-that-be agree that it is a bug then it should get fixed so that no toc.ncx tweaking would be necessary. Sometimes these things get fixed very quickly, occasionally they don't, so don't hold your breath.

Good Luck