udev existed before systemd, but was merged to it sometime in 2014. By quick Googling there are still several forks that maintain it as a separate component.
I personally don't think it's that much of a trouble to just journalctl for the /dev/sdX of the inserted device and then sudo mount /dev/sdX /mnt/tmp manually, because I so rarely plug USB drives. For permanently attached or frequently used devices you can add them to fstab and mount by UUID to a fixed path.
Either way, you will still always need to umount manually or risk loosing data.
I expect there are some distro-specific hoops to jump through, but I have no idea which ones -- I really don't like automounting, I keep it disabled even on KDE.
(Why? Old habits die hard, I guess?)