linux - Enabled WOL - Now my computer powers on by itself

To use the wake on LAN feature of my onboard network interface, I had to enable "Wake on PCI-Express" in my BIOS settings. WOL works fine now.
The only problem is that my computer turns itself on without me sending a MagicPacket. Sometimes it happens only a few seconds after I shut it down using "poweroff" or "shutdown -h now". Sometimes it "waits" for one or two minutes.
I have disconnected all unnecessary components. Only power, display cable and ethernet are left.
I use Proxmox (Debian) and have set it up to enable WOL via

ethtool -s eth0 wol g

"g" is to be used if you only want a MagicPacket to be able to wake up the machine.
Is there anything I have to do before I shutdown the computer to prevent it from waking up by itself?

Thanks for your help,

Kevin

UPDATE

After I shut down the machine it seems to power itself on only one time. When I turn it off after that, it stays off. Also the source for the wakeup seems to be "inside" the computer. When I unplug the ethernet cable immediately after shutdown, it powers on nevertheless.

UPDATE #2

Last night I gave up and installed an old PCI NIC. I disabled "Wake on PCI-E" and enabled "Wake on PCI". Everything works fine now using WOL to wake up the machine via the second NIC.

Before that I already tried several other PCI-E NICs (Intel, Broadcom, D-Link).