The presence of 3s in a 4/4 bar is not always indicated by the actual number 3. Sometimes its presence lurks in a dotted eighth, sometimes in a three-sixteenth "beat" following a sixteenth rest. Three of something plus five of something else is as much eight as two times four. But the feeling is totally different.
The feeling is what agitato refers to, not agitation in our frenetic literal sense of the word, but in the sense of a structured non-structure.
