Do your use IR remote in same room as NUC, such as for Xbox or maybe some TV like Philips? If so, it may be the reason for power on. You could try something like temporarily covering the front right part of the NUC with cardboard/thick non-clear tape. Again if so, the latest BIOS have some options to disable that CIR power on from various states. Regarding Wake on LAN, rather than just BIOS you should look for such settings in the Properties-Power tab of the device drivers for network adapters (both wired and wireless).
Thank you for the response. I don't have an IR card installed so I don't think that's the issue. I'll check the CIR power on options.
You say "I don't have an IR card installed..."
The NUC comes with IR installed, it is the little window to the right of the headphone jack on front right of case. Maybe you meant that you did not install CIR device driver, but the following "power up" situation happens from "BIOS" regardless of whether device driver is installed.
Unexpected power up is something which drove me crazy when I first got my NUC. Earlier Windows-based HTPCs would power up with normal non-IR power button and then when you added IR, the IR remote button would cause it to sleep or wake from sleep (not from shutdown state). The NUC added IR power up from shutdown state. Only recently in the BIOS did the NUC allow disabling that feature.
Frustratingly, when that feature came out in BIOS and I disabled wake from S5, I now often have to press my IR button multiple times (not just once) to get it to wake up from sleep - can't "swear" to it, but sure seems that way - not sure why.