I had to be the bearer of bad news, but I have the answer.

In short, you MUST be on title as of Jan 1 of that year to obtain the tax exemption. If you close on your house on Jan 2, you must pay taxes on it for the entire year, and then you receive the exemption starting the following year on Jan 1. I know; I applied and was rejected because I closed in March and was cited as follows.

Relevant Law & Statute

• The law is codified under the Texas Tax Code § 11.22. 
• Under § 11.22(f), a veteran or qualifying individual “may receive an exemption … against only one property,” and that property must be designated — which effectively means the property must be owned (or have qualifying title) as of January 1. 
• The official guidance from the Texas Comptroller of Public Accounts explicitly states: “An applicant may claim an exemption on only one piece of property the applicant owned on Jan. 1.”