Tricks Tricks:
One adjustment to the above, for finds committing it doesn't always need to be start to finish. For something like shoplifting it needs to be start to finish so that you can ensure they didn't bring the item they're stealing with them. For something like murder, you don't need to see them start repeatedly stabbing, seeing them in the middle of a stabbing spree is good enough. Additionally something like child pornography is always in the process of "committing". So if you were to use a friends laptop and find some kiddie porn, it qualifies as "finds committing".
Either way, this guy in no way has the colour of right to attempt a citizen's arrest of someone, and could easily be sued for attempting it.
True, for legal purposes we usually preach the start to finish, you are correct; if you come in on someone stabbing someone, yes; you found this person committing an indictable offence. However, I would recommend against attempting the Citizen's Arrest in this case.