Headers (and footers) are Section properties so it is important to know what section breaks there are. To see section breaks you need to go into draft view. (Displaying non-printing characters will display them too, but not as distinctly.) The new page section breaks are easy to spot but the continuous ones can be much easier to spot when in draft view. (Draft view was called normal view in earlier versions of Word.)

See Sections / Headers and Footers in Microsoft Word 2007-2013. I know of no differences in how h/f work in Word 2010 and 2013.

Assuming a single section (which is what a new document starts with) if you set the headers/footers for different first page, you will be able to start a header/footer on the second page of the section.

How many pages are there in your document? My guess is that you have a new section starting somewhere on the second or third page.

Here is another good reference on Sections: Working with Sections (or Why Word appears to behave so illogically when you delete or move a section break or How to preserve section formatting when pasting between documents) by Dave Rado, MVP.