I don’t think Scrivener is setting the two-page layout setting in the ODT files (or more accurately, the Aspose conversion engine that it uses to convert from its native RTF). At least, in my copy of LibreOffice on Linux, they load in single-page layout.
I’ve tried exporting an ODT from Scrivener, and decompressed it, loading the settings.xml file and saving that externally as a reference. I then loaded the ODT in LibreOffice, deliberately changed it to two-page book layout (using the third button, closest to the zoom slider), and saved it. I then examine the two copies side by side, and found this setting in the copy saved by LO:
<config:config-item config:name="ViewLayoutColumns" config:type="short">2</config:config-item>
<config:config-item config:name="ViewLayoutBookMode" config:type="boolean">true</config:config-item>
These lines are an addition, they weren’t specified at all in the original copy, and I’ve confirmed they are the responsible settings for this. If I change the columns to 1 and the book mode to false then I get the typical single column of pages look. If I set the columns to 3 and keep book mode false I get three pages across, but no recto/verso emulation.
Anyway, that’s probably all way more of a technical answer than you needed, but if you know how to unzip .odt files and examine their contents, then you could at least verify if your exported copies are the same. There may be a default you can change somewhere? I ran a few quick web searches but didn’t come across anything to share, but I am running a slightly older version (Debian life).
As an aside, it is not too difficult to get Scrivener for Windows running on Linux these days.