Just to close this issue, the "New window" flag was missing from the hyperlinks, because Word gave the implication that they were present, even though they weren't.
A quick way to check if a hyperlink points to a new window is to press <Alt>+<F9> to show field values.
You should see the \t flag with target value "_blank" after the URL for the hyperlink. See the screenshot below.
The reason Word seems to confuse matters is that in the "Set Target Frame" dialog box, if the checkbox "Set as default for all hyperlinks", is clicked after selecting "New window", the field contains the text "Page default ( New window )", but in fact the required flag '\t "_blank"' is not set. See below.