Yes, the rule is correct, but I don't think "Alex" has an "s" or a "z" sound at the end. It is a "cks" sound, or "ex" sound. Therefore, it would be Alex's pen, or Alex's answer. Now there are exceptions for ancient names and for owner preference...but I don't want to confuse you...Bob
I worked with two former English teachers who kept us up-to-date on English grammar and punctuation rules. I don't like the new rules, but they are to always place "apostrophe s" after a word that ends in s. In fact my state passed a law that we had to follow this rule when we were making Arkansas possessive in drafting and editing our state's laws. It is now officially "Arkansas's".
I tell this because the new rules would also automatically place apostrophe s after Alex to make it Alex's.