This behaviour is the same on Windows. If Windows doesn't receive a DHCP address is will assign one in the self-assigned range first. After about a minute or so it too will re-request an IP address from the DHCP server and if it receives one it will assign that to the interface.

What Windows does do wrong is that it then also drops the self-assigned IP address which may already be in use for communication, this can cause issues with other hosts that are communicating with it over zeroconf.