PS: I am not sure whether the microphone jack pinout is the same as drawn. Anybody can confirm whether this is right (the microphone jack from the headset is rose-colored and the earphone jack is green-colored)?
There is no 100% sure answer to your question. Because we (and maybe you?) don't know exactly what microphone you are talking about and how it is wired. There is more than one convention for wiring microphones to TRS 3.5mm plugs.
I would first try connecting just the tip of the mic connector to "Microphone" ring on the iPhone. And if that doesn't work, I would connect BOTH the ring and the tip together to the "Microphone" ring on the iPhone.