The passage cited from Carlisle comes from a 1902 newspaper reprinting of selected entries from his wartime diary. He, Thomas J. Carlisle, was the editor/publisher of the Weekly Enterprise (Enterprise, Ala.) at that time, and he was trying to solicit his remaining fellow regimental veterans to send him their recollections by printing selections from his own diary. He'd served as a Lieutenant in the 37th Ala. Volunteers during the war.
Since the newspaper account comes 50 years after those events occurred, perhaps the "northeast" directional mistake is that of a typesetter, or a transcriptionist, (or Carlisle himself) misreading the word "southeast" from the old handwriting in the antique source document.
I guess it might also be that Carlisle could have "misremembered" the direction all those years later (or maybe didn't know all that much at the time he wrote in his diary) about his surroundings at Columbus.
Of course, this is all pure speculation. It would only be possible to solve if one could locate and carefully inspect Carlisle's original diary instead of having to rely on the 1902 published newspaper version, and even then, it might still say "northeast" as plain as day!
-Chip
(PS, My late father-in-law was an old-line newspaper man and "set" a lot of type by hand as recently as the 1960s and told me some pretty funny and interesting stories about mistakes involving line upon line of backward-facing individual letters of "hot type" and the accompanying "California job cases" of loose letters and fonts [which drove him to distraction], so I guess one should never disregard just how many fallible humans it took to print them when it comes to reading those old newspapers)