the website you gave me states that if NaOH is in excess by one drop - then the solution will turn pink - but it is not in excess.
In a way you are correct. After neutralization solution should be neutral.
Am I to assume (as stated further down in the article) that the excess drop is present to show that all acid has been neutralized?
Yes. That's what titration is about, that's what the question is about.
Problem is, we don't know if the solution has been neutralized till we see the color change. Then we have already added some small excess of NaOH, so technically we are past the neutralization. However, excess needed is neglectable (see discussion at
http://www.titrations.info/titration-end-point-detection and
http://www.titrations.info/acid-base-titration-end-point-detection).