Icom A24 w/ PTT and headset mic

I use my A24 lots, for listening to ASOS, communicating to aircraft at
fly-ins, ordering fuel, etc... I rarely use it with a headset.

The other night, I had a full-on comm failure and needed to use it
while aloft, with a headset. It took me a few minutes to remember,
but my radio keys only the radio's onboard mic when keyed with the
onboard PTT, not the headset mic. To use it with a headset, I need to
put the radio to my mouth and talk into the radio, the mic in the
headset is not used. My adapter is a genuine Icom product, with
phones, mic, and PTT connections. I'm only connected to the phones and
mic jack.

Can anyone confirm to me that an external PTT will in fact key the
headset mic?

My Googling has come up with lots of yeas and neahs in conflict.