Move Action in CSP not working when Perform Recruiting Candidate Selection Process Actions is run

Summary:

We have a requirement where we have to move an application from one Phase/State(Let's say A) to another Phase/State(Let's say B) depending on certain conditions -value of a Candidate Extra Information field which is updated by another integration(Let's say XY).

For this I have used Move action and added to Source Phase/State. I have also added the fast formula. In our scenario, this move does not happen immediately when a candidate lands on A, but should happen when the integration - XY updates the Extra Information Field.

So our understanding is that when we will run the process - Perform Recruiting Candidate Selection Process Actions , system should move the application from A to B upon satisfying the condition.