Major General RH Milroy was in command in Tullahoma during the period in question. He has a diary and several letters that describe him using Lt Col Stauber and the 42nd MO as his hit men in his battle against guerrillas in the Tullahoma area. Orders such as "make sure you leave them dead" and hanging without trial were common actions. His plan was to cleanse the "poison" from the community using "fire and blood".

There is at least one order with specific kill orders of named individuals given to the 42nd.

Milroy was known as a brutal man and terrorized the Winchester Va area after 2nd Bull Run before being sidetracked to middle Tennessee after getting whipped by Ewell's Corps at Winchester. See: https://vtechworks.lib.vt.edu/server/api/core/bitstreams/9d38f9d7-39ee-4a6b-b61b-6694c95a3aed/content

He was impressed with the way guerrillas were handled in Missouri and wanted to emulate the process including banning, removal, and drum-head courts and executions. He referred to it as the "Guerrilian-Mo. style" in a letter to his wife Mary.

See Tennessee in the Civil War: Selected Contemporary Accounts of Military and Other Events, Month by Month by McFarland (2014) for more and Milroy's personal papers are digitalized.

There are lots of little strings to be pulled in this hunt....

So given who was in command it is perfectly feasible that members of the 42nd if convinced they had Centralia participants in hand just out and out executed them without trial, paper trail, or orders per se. They would have been lauded by Milroy. The hunt continues.