The general advice for keeping SSD drives at optimal performance is not to put the /tmp partition on one.
So I have root on the SSD drive and swap, tmp and home all on the SATA platter drive. This means I can have a relatively cheap 30GB SSD drive and an older 500GB SATA drive.
The answer to my question appears to be yes, both distros have zero problem with using the same /tmp partition. Or at least, thus far both have behaved as expected.