Prevent external monitors from turning off when Mac is locked
I finally managed to pinpoint the issue: Display Port cable.

One of the monitors were connected with a Display Port to DisplayPort cable. After switching from a Display Port to Mini DisplayPort cable, everything seems to work properly.

One monitor is connected via HDMI (from dock) -> HDMI (monitor 1 input); the other via DisplayPort (from docking station) -> Mini DisplayPort (monitor 2 input).

This also meant that I had to change monitors, because the aforementioned AOC monitors did not have a Mini DisplayPort. I'm now using 2 x Lenovo ThinkVision monitors (model: P27q-10).