catch (one) in the act
To see, and perhaps apprehend, someone as they are doing something (often something nefarious). The police caught the robbers in the act of ransacking another house. I suspected that my friend was stealing money from me, and then I caught her in the act.
caught in the act
Seen, and perhaps apprehended, while doing something (often something nefarious). Our security cameras caught the burglar in the act.
caught in the act
and caught red-handedFig. seen doing something illegal or private. (See also catch someone in the act (of doing something) and catch someone red-handed.) Tom was caught in the act and cannot deny what he did. Many car thieves are caught red-handed.