I looked over the censuses you mentioned for Rebecca Carroll for 1880 and your 1900 Rebecca A. Simmons in Attala County is not the 1880 Rebecca Carroll living in Simmons household in Scott County. If you look at the 1900 census for Scott County MS a Rebecca Carrol b. Jan 1845 with Carrol children Alonso B., Lottie F., Berta, and widowed son-in-law C.B. Reeves and a grandson Carrol Reeves in household. Looking at the neighbors names it looks like the same house too from 1880. In 1910 MS Scott County census still there as Mrs. R.A. Carroll with children still in household and in 1910 MS Attala County there is Rebeca Simmons and "adopted son' James Simmons.
So that means the widow Rebecca A. Simmons of Attala County MS does not have the maiden name Simmons, and would still need to be found.

Also looking at 1880 census again I gave you the wrong James W. Simmons (jr) listed as cousin with an (wife)Allie too. They are listed in Find A Grave of Attala County MS both died before 1900. I redid my search as Sim* and found a J.W. Simmon age 66 with wife Rebecca age 36 living in Newport, Attala County MS. And looking at 1870 MS Attala census J.W. Simmons is a widower with children in household so Rebecca would be a second wife.

As for telling census and filing Draft Card with birth in Newport, Attala County MS, some adopt the birth place of the state one is adopted in or was naturalized in. It complicates one life to say one was born outside U.S. It could also be he was not aware he was born in Ireland till later in life. What does his death certificate say? Have you found Rebecca's ?