xscreensaver on 18.10 MATE - not starting

At first you should remove other screensavers (MATE Screen Saver in your case) from system to prevent interference:

sudo apt purge mate-screensaver mate-screensaver-common

Then enable XScreenSaver autostart via systemd user's service:

systemctl --user enable xscreensaver.service
systemctl --user start xscreensaver.service

   Note: for debugging you can use systemctl --user status xscreensaver.service.

Then wait for timeout and screensaver activation.