Interpretation of block diagram for proportional feedback system with respect to time
Unless time-dependency is specified, assume there isn't any.

Nothing in your diagram seems to mention time at all.  You can therefore assume each block does whatever it does instantly.

Of course in the real world, there will always be some time delays.  Part of knowing how to design good control systems is to know when these delays matter and when they don't.

In general, you want the dominant time constant to come from the plant, with the controller itself being faster.