Wirt Adams' Cavalry Regiment is the 1st Mississippi Cavalry.
You may notice there's quite a bit of difference between the two snippets of text that have been quoted here.
"Col. Wirt Adams reported to Gregg during the night of the 12."
With McPherson's cavalry chasing Gregg on the direct road to Mississippi Springs until dark, this would imply that Adams rode to Mississippi Springs via Clinton.
"I marched by General Gregg's order to Raymond, and fell in his rear."
This would imply that Wirt Adams' 800 men joined Gregg in time to do some rearguard fighting. In addition, it appears that six companies of the 20th Mississippi (about 400 men) were with Adams at Dillon's Bridge and reported to Gregg at some point during the day ... according to the regimental history (date appears to be incorrectly noted as May 14th).