We do if the offense occurs on private property. It's my understanding that the Minutemen operate on private property, at the request of, or with the permission of the landowner. The people are trespassing as well as entering the country illegally. The MM report them to the authorities. Just like you can, or could, call the highway patrol on your CB or cell phone to report a speeder or reckless driver, and you don't even have to be on private property to do that.
The bottom line is the the MM are doing their ordinary civic duty, reporting misdemeanants to the police or sheriff. Now if the law breakers are committing a felony, witnessed by the citizen, such as aiding or inducing someone to enter the country illegally, then the citizen may make an arrest, at least in most states and jurisdictions, and certainly under the common law.
Excellent analysis.