I'm not sure what you mean by "properly" but didn't initng and upstart (and probably some others I can't recall) do the parallel stuff before systemd?
but the "faster boot" you're remembering are actually a joke at the time. since the team working on it were probably booting vms all the time, the system was incredible aggressive on shutdown and that was the source of it. something like it reboots so fast because it just throws everything out and reboot, or something. i don't really care much for the jokes but that was why everyone today remembers "systemd is fast".
Nowadays if you start anything more serious from your user session (e.g. start a qemu vm from your user shell) it will get SIGHUP asap on shutdown, because systemd doesn't care about non service pids. but oh well.
...which is where the jokes about "systemd is good for really fast reboots" came from mostly.
It's trivial to run these as a user service, which can linger afterwards. Also, systemd has a configurable wait time before it kills a process (the "dreaded" 2 mins timer is usually something similar)