Asunción

The "u" is pronounced as in the word "put" and NOT like "umbrella." Therefore, according to the key, proper pronunciation is as follows: ah-suwn-THYON (Spanish), ah-suwn-SYON (Latin American Spanish).

Actually, no that is incorrect. The Spanish U is pronounced like a double oo in English. Which would make the pronunciation ah-soon-THYON (Spanish), ah-soon-SYON (Latin American Spanish, as stated on the names main page). There really isn't an "uh" sound in Spanish.

The last syllable isn't "SYAWN" or "THYAWN"; it's "SYOWN" or "THYOWN" (rhymes with "throne").

Actually, it's somewhere in between. The Spanish "o" is a pure vowel rather than a diphthong, as in most English accents, in which it is something like "uh-oo" or "eh-oo." "Aw" is closer, again as long as you don't make it a diphthong like "aw-uh." (It should be about like the o in "song" (but not "saw-ung.")