Not sure about your use of FUSE, but mount propagation (aka shared mount volumes) work with vanilla docker.
Here is an example:
// Setup a volume with shared mount propagation
$ mkdir /tmp/shared-volume
$ mount --bind /tmp/shared-volume /tmp/shared-volume
$ mount --make-rshared /tmp/shared-volume
// Start a docker container that will consume mounts within this volume
$ docker run -d -v /tmp/shared-volume:/tmp/shared-volume:rw,rshared --name consumer busybox sleep 1000
// Start a docker container that will create a mount
$ docker run --privileged -v /tmp/shared-volume:/tmp/shared-volume:rw,rshared ubuntu bash
root@3bf88c9ffcb3:/# mkdir /tmp/shared-volume/tmpfs
root@3bf88c9ffcb3:/# mount -t tmpfs tmpfs /tmp/shared-volume/tmpfs
// Exec into the 'consumer' container to find that the newly created tmpfs mount is available.
$ docker exec -it consumer sh
/ # stat -f /tmp/shared-volume/tmpfs
File: "/tmp/shared-volume/tmpfs"
ID: 0 Namelen: 255 Type: tmpfs
AFAIK, this should work for FUSE as well.