I am as perplexed as you are then -- this ordinarily should not happen. Temporary hit points are lost first, CON based hit points are lost last. The only possible scenario I could think of is that it would be possible to buff someone who's near-death with temporary hit points, then lower that someone's constitution (lose a buff or actual ability drain), and get into this "life only by temporary hit points" situation. But this is not what happened, as you describe it.
The only way I can think to test the temp hit point + constitution decrease would be to do something like activate barbarian rage, take damage, drink a potion of aid, wait for the rage to wear off, and all you have left health-wise is temp hit points, then see what happens. It could be that the bard song buff is uniquely scripted in PoTM (since the description in the wiki is different from the vanilla game) and it adds HP differently (or is buggy).