New Page > New Odd Page kills Span Columns

I have a style called H1-new-page. That is, Heading 1, and specifically to start on the next new page. (Occasionally I want to use H1 without the new-page, so I have a separate H1 style for that.)

I have it set to span columns. Works fine every time, and looks like this:

After some reflection, I decided that there are both graphic design and efficiency issues (in particular, not having to deal with graphics that extend into the margin away from the spine suddenly extending into the margin towards the spine) to make a duplicate of this style, called H1-new-odd-page. Unsurprisingly, it is exactly the same as H1-new-page except that, instead of starting on a new page, it starts on the next new odd page. But this is what happens:

Yes, it now starts on the next odd page. Perhaps because of the word "odd" it shows odd behavior: the heading, which still says to span all columns in the paragraph style (or if I switch it to span 2 columns) instead spans no columns.

If changing from H1-new-page to H1 new-odd-page moves the text from an even page to an odd page, it doesn't span columns.

If changing from H1-new-page to H1 new-odd-page does not move the text from an even page to an odd page, it still spans columns.

Is this a bug or just a feature I just don't understand?