2> then you have taken some action (Approve/Reject),
3> Your concern is: "when you have taken the action, Case has not proceeded as expected."
Possible fix as below :-
1) Email which you have received should have message into it, so that you can get the Message Data to process it. Once you get the Message data Map it to the appropriate required clipboard Page property. (It may require parsing or need to do substring to get actal value so that you can handle your logic)
2) Now when you get the data on Page, you can refer that page property in your When condition, then refer the when rule into your flow.
you have understand ;) for the automatically process the case, when the email service process the email response i must to modify the activity "pyCreateAndManageWorkFromEmail" that i use in the EmailService ( image attach ).
Yes, you have to modify your Process, instead of updating "pyCreateAndManageWorkFromEmail" create separate activity(ex:- ProcessEmail), In the "ProcessEmail" call "pyCreateAndManageWorkFromEmail" then handle your required logic in later step,
Some Debugging steps:-
Trace the activity "pyCreateAndManageWorkFromEmail" see on which Page property your required value is comming, then do set in your created page so that you can handle it in further process.