The messages weren't private messages they were channel messages but pretty sure that wouldn't make a difference. Messages I sent from my ZNC (nickname: ekcdd) appeared correct to me and to the direct mIRC client (nickname ekcdd_), however messages sent from the direct client were wrong on the ZNC connected mIRC so yes, it's only incorrect on the ZNC connected mIRC.
My ZNC isn't hosted on my local network but is located in the same state as myself, hosted on a VPS and the Linux box reports the timezone as AEDT +1100 (same as my local machine, this was something I only checked today)
While confirming all the information you provided, I did another check, however the times now match and is displayed. This error happened right after we entered DST and mIRC was running during the transition. The timestamp 2020-10-03T17:16:15 seems to be 4:16AM (which is the correct time, so mIRC is adding DST maybe?)
Also I checked what timestamp the ZNC is currently send and it appears to be sending 2020-10-07T16:37:25.810Z and the local time is 3:39 am
I think I covered everything, if not I'm happy to cover anything I missed.