It sounds like you missed a step. You need to create an apt conf file that runs unattended-upgrades (in addition to the configuration you already did in /etc/apt/apt.conf.d/50unattended-upgrades). There are a lot of options (see /usr/lib/apt/apt.systemd.daily for a description of options; the manpages are lacking), but just running:

  dpkg-reconfigure unattended-upgrades

will create a minimal config file, '/etc/apt/apt.conf.d/20auto-upgrades' that may be all you need. But, you might consider adding something like below to cleanup downloaded package files:

  // Auto cleanup archives
  APT::Periodic::MaxAge "10";
  // Setting minage too is a good idea to prevent race conditions
  APT::Periodic::MinAge "8";

Or, if you prefer (but, this will delete all archives present when it triggers and not just old ones like above):

  APT::Periodic::AutocleanInterval "10";

(Note: I'm assuming Raspbian is the same as the upstream Debian; I've never used Raspbian)