Q:

merging a tag into a synonym'd tag creates that tag again?

On this post at Math.SE, one sees that it is tagged both with (multivariable-calculus) and (vector-calculus). If one clicks on the (vector-calculus) tag, one gets redirected, correctly, to the page for (multivariable-calculus), as for a long time the (vector-calculus) tag has been a synonym for (multivariable-calculus). 
Problem: why does the post still contain both tags, instead of them collapsed into one?
What caused this:

Mark and merge (tag-2) as synonym to (tag-1).
Given a question tagged with (tag-1) and (tag-3), merge (tag-3) into (tag-2). 

Ideal result:

Question is now tagged as (tag-1) only. All questions previously tagged under (tag-3) is now tagged (tag-1) instead. 

Observed result:

Questions tagged with (tag-3) now is tagged with (tag-2), which displays as a different tag from (tag-1), but links to the same page. 
(tag-2) now appears in the Tool panel for "new tags" as a new-tag, even though the link that it creates points to (tag-1). 

A:

If you make tag-2 a synonym of tag-1, you are not removing tag-2 from questions. Future questions using tag-2 will automatically have tag-1, but that doesn't change already asked questions.
tag-2 and tag-1 are still two separate tags, if you make them synonym, and there are already questions using tag-2.
To obtain the result you wanted to obtain, you should:

Merge tag-3 with tag-2
Merge tag-2 with tag-1
Make tag-2 a synonym of tag-1

In your case, you just need to merge tag-2 with tag-1.

