The info you requested, about Texans who served in CSA militiary units outside Texas, can be found on the following web site:
But make sure you specify "resident of Texas" and "state served" with the other input as general as possible such as entering "g" for a first name in lieu of "George", etc.
I entered the names of a few Red River County men and a Tennessee military unit popped up.
And yes, this is also new to me since I did not learn to use the Internet until I had a hardcover book in hand; otherwise I would have never finished my 1,022-page book. (I must quickly add that my 4 helpers found answers for me on the Internet as I requested. .. They did this because I was transcribing, interepreting, and indexing handwritten original records that they thought should be incorporated into Texas written history.)
P.S. As you may know, I have 38,500 entries of mostly Texas State Troops in my 134-page Name Index (some men's names appeared on more than one page[entries]).