If I'm not mistaken, yes.
How I understand it is that when an attack inflicts a status, the position of the ninja decides who chases first. It prioritizes the ninja who's at move 1 (M1).
If your M1 ninja doesn't chase that particular status then your M2 will. Then it goes on with M3 and M4.
If your M1 and M2 both chase knockdown, M1 will move first.
Let's say your M3 chases first (eg: knockdown to repulse), if your M1 has a repulse chase then M1 will move.
tldr; after every inflicted status the combo will prioritize M1 before M2 and so on.