Every Section in a Word document has three headers and footers: primary, first page and even page. If your document's page layout has the:
• 'first page' option checked, it will have both the primary and first page headers & footers
• 'even page' option checked, it will have both the primary and even page headers & footers
• 'first page' and 'even page' options checked, it will have the primary, first page and even page headers & footers
in every Section. There is no connection between what appears in, say, the primary header and a first page or even page header.

Furthermore, in any given Section, each given header & footer can either continue whatever is in the previous Section's corresponding header or footer or start with content of its own.

Your problem description suggests your document's page layout has the 'first page' and 'even page' options checked, plus multiple Sections. The first question to ask yourself, therefore, is whether your entire document (or even any of it) requires that configuration. If not, simplify the page layout to the minimum necessary. Then, if you do need more than the basic page layout without the 'first page' and 'even page' options, plus headers/footers, each of those headers & footers will require their own content.

__________________
Cheers,
Paul Edstein
[Fmr MS MVP - Word]