Deleting across section breaks in Word gets you the next header.
This is a Word issue, not an AutoTag issue. But people trip over it so we're covering it here.
Word stores all information for a section break, including the headers/footers for a section, at the end of the break, not the beginning. Therefore if you delete from the middle of one section to the middle of a subsequent section (which includes the case of deleting to the end of the document), then the section you started the delete on will have it's settings change to those of the section you ended the delete on.
In other words, if you delete from the middle of section2 to the middle of section 3, then section 2's headers/footers will be discarded and it will now have the headers/footers from section 3.