Where is my /tmp mounted?

If the output is as above, it's on the hard disk. You can get /dev/root by looking at the kernel commandline:

$ cat /proc/cmdline | grep root
BOOT_IMAGE=/boot/vmlinuz-3.19.0-32-generic root=UUID=0cde5cf9-b15d-4369-b3b1-4405204fd9ff ro

So /dev/root is equivalent to the partition with the UUID printed above; your's will differ. To look this UUID up, use

$ sudo blkid
/dev/sda1: UUID="0cde5cf9-b15d-4369-b3b1-4405204fd9ff" TYPE="ext4" 
/dev/sda5: UUID="37bc6a9c-a27f-43dc-a485-5fb1830e1e42" TYPE="swap" 
/dev/sdb1: UUID="177c3cec-5612-44a7-9716-4dcba27c69f9" TYPE="ext4" 

As you can see, the matching partition is /dev/sda1. So your /tmp is on the hard disk. Another giveaway in the output of df is the mountpoint /. If you mounted /tmp in the RAM, you'd instead get

$ df /tmp
Filesystem     1K-blocks  Used Available Use% Mounted on
tmpfs            3640904    20   3640884   1% /tmp

The output of df /tmp gives the answer: the “Mounted on” column lists /, so /tmp is part of the filesystem that's mounted on /, i.e. the root filesystem. It is not a separate filesystem.

To be more accurate, you should run df /tmp/: if /tmp is a symbolic link, then df /tmp lists information about the location of the symbolic link, whereas df /tmp/ lists information about the target directory.

The mention of /dev/root in the device column is due to its being listed in /etc/mtab. You can find the real device by looking in /proc/mounts with </proc/mounts awk '$2 == "/" {print $1}' or findmnt /.