Some quotes from OR's.
This explanation comes from Confederate General Chalmers.
"… This was accomplished easily and in good order, each brigade forming alternately in rear of the other until we were out of reach of the enemy, when we moved slowly by the eastern road back to Quinn's Mill, and crossed Coldwater."
"… Received an order from General Chalmers to move around to the support of Colonel McCulloch, who by this time had become closely engaged by the enemy's left. Moving rapidly to the right, I took position in rear of Colonel McCulloch, who withdrew upon the Mount Pleasant road; thence on the road to Quinn's Mill, on Coldwater, the enemy pursuing us closely with two pieces of artillery."
"The enemy pursued us with his artillery and a small force on the road, while his cavalry moved down the western road and endeavored to cut us off, but did not succeed. The Seventh Tennessee (CS) (Colonel Duckworth) was placed on that road to hold them in check until our column crossed."
"After Duckworth crossed the enemy came up to the river and opened a furious fire of small-arms, which was soon silenced by Captain Bledsoe with a few shots from his rifled gun, by which, it is said, he killed 7 men and 15 horses."
This is the Second Iowa Cavalry's description of the pursuit, and their meeting the Seventh Tennessee Cavalry(CS).
Lieut.-Col. Hepburn now mounted his command and gave chase, company "K," Capt. C. P. Moore commanding, taking the advance. The chase was exciting. It was ten miles to Cold Water, where the rebels, being reinforced, made their first stand. This entire distance was traversed by both parties on the gallop. Lieut. Jacob F. Bandy, commanded the advance platoon of company "K." He overtook the rear guard of the enemy at the edge of Cold Water bottom, where they had attempted to make a stand.
Our boys charged after the retreating foe until they came face to face with the main line of battle, which the enemy had by the aid of reinforcements been able to form on the bank of Cold Water creek. The skirmish line was on the north side of the stream, which was the side from which Bandy was advancing, while their main line was on the south side. As the creek was very difficult to cross, this gave the enemy great advantage. As it was now after dark, Bandy with his platoon of sixteen men ran up to within ten or fifteen steps of the rebel line before he discovered them. He was not long left in ignorance as to their position, however, for no sooner had he attained this distance, than he was received by a volley from the entire line of several thousand; but fortunately their aim was too high and no one was hurt, while the light made by the flash of the guns, revealed the situation and force of the enemy. Although Bandy had but sixteen men, while the enemy were numbered by thousands, he did not give back, but springing from the horses, the boys took shelter behind trees, logs and stumps, and awaiting the fire of the enemy's guns to give them light, they used their carbines to a good purpose, while the main force was formed and sent up to their support. For an hour the fighting was sharp, each side firing at the blaze of the others guns, when finding that nothing could be gained by continuing the contest, Hepburn ordered the forces to be withdrawn. Capt. Chas. C. Horton was wounded in this action. The forces fell back to the first plantation and camped for the night.
The next morning Hatch came up with the balance of the brigade, and the pursuit was continued until the enemy reached the south side of the Tallahatchie (River), after which the brigade returned by way of La Grange, where they remained for several days. The Federal loss in this campaign was five killed, twelve wounded and twenty missing. The enemy left forty-one dead on the field, and we captured fifty prisoners; their wounded could not fall short of 200. Among the prisoners were eight commissioned officers, including one Brigadier General$. We found our camp equipage at Colliersville, which place we reached on the 14th of November, 1863.
$ - Again, Union reports are confusing Colonel George as being a General.
The Tallahatchie River was the "boundary" for the Confederate forces, located between Holly Springs and Oxford. During winter and flood stages, this river had few places to cross. In the 1900's, the river was dammed to form the Sardis Lake.