Deleting content of /private/tmp moved on different HDD

I have a Macbook pro with 2 internal HD (stock HD for data and data doubler + SSD in place of the optical drive, hosting the OS). I'm now trying to optimize this setup to take into account the presence of the SSD, and I want to move the temporary folder from the SSD (/private/tmp) to the secondary drive (/Volume/MacintoshHD/private/tmp).

Following this (http://ift.tt/1GEa2eu), here's what I did :

sudo ditto /private/tmp /Volumes/MacintoshHD/private/tmp
sudo rm -rf /private/tmp
sudo ln -s /Volumes/MacintoshHD/private/tmp /private/tmp

Everything is fine, but when I reboot, I expect the folder to be emptied as usual. However, I found out that whatever files that were present on the previous OS execution are still present.

My guess is that whatever script emptying the /private/tmp folder executes before the magnetic HD gets mounted, which means that the link pointing to the tmp folder does point anywhere then, and hence the failed deletion.

Any idea how to fix this? Any other suggestion to move the /private/tmp folder to another drive and still preserve automatic deletion?