I had the issue where my microphone wasn't being picked up from my Turtle Beach X1 headset.
This headset is a few years old now, it comes with a green 3.5mm and pink 3.5mm connector, one for headphone and one for microphone.
There is also a control box which takes a cable out into the game controller with separate mute and voice chat volume. The cable is a funny semi circle fitting at the controller end but in essence a 2.5mm plug.
Plugging the pink 3.5mm connector will not work as the connector isn't TRRS enabled (if you google this you will see a series of revisions on the 3.5mm connector and it can be separated into different zones), looking at several connectors against each other you will notice extra black bands around some of them. The 2.5mm to 3.5mm conversion cable that comes with the MS adapter demonstrates what the new type plug looks like.
I purchased a 2.5mm to 3.5mm cable in haste to plug into the TB and MS adapter but all this did was cut off Kinect and didn't actually give me any voice still. Examining the cable it wasn't TRRS enabled with the 4 zones, only had 3 (TRS).
What put me onto looking at connectors was a revelation when my blackberry headset that came with my phone actually worked and this was the new style 3.5mm connector.
I therefore have this solution which may work well for others. If you have a 3.5mm connector for your microphone the chances it being the new connector is remote (newer headsets possibly combine these). You can get a cheap extension cable with female/male 3.5mm ends to take it from TRS to TRRS specification and it should work. I guess those with a 2.5mm connector can use the MS supplied cable the comes with the headset adapter and are currently not having any issues?
I actually purchased the TB 2.5mm to 2.5mm cable as it has inline mute and volume controls (yes I know you can do these on the MS headset adapter too), then I plug the one end into the TB control box and the other into the supplied MS cable (female 2.5mm to male 3.5mm) that in turn goes into the headset adapter. Important to note my TB cable is not the new standard but plugging into the MS cable converts the microphone into the correct zone that the headset adapter acknowledges/recognises.
If you do have any questions about this happy to try and help out. I managed to get away from spending on another headset for the XB1 and can now use my TB on both platforms.