But, we can draw some reasonable conclusions based on what we know so far. The Tristar controls USB functions, including data transfer and charging. The Tristar can be damaged by using non-Apple certified lightning cords because cheap cords lack a voltage regulator found genuine Apple cords or Apple certified cords, thereby potentially exposing the Tristar chip to voltage spikes and subsequent damage. Now plug the fan in, what's occurring? Instead of the phone pulling current from a charge cord, the fan is pulling current from the phone. This current passes through the Tristar the same as if you were charging the phone. Hypothesizing, can the Tristar handle current passing through it in reverse? Is the fan pulling more current than the Tristar can handle? Further testing once we have some fans is needed.
In the meantime, sitting on my desk is an iPhone 5S with a bad Tristar chip after using one of these fans. Similar events have been reported around the United States and the world. Lenny Jenkins of The Gadget Lab in Ohio said that he's, "I heard the same thing, those things are killing devices" when it comes to fans ruining cell phones. James Worrall of Technology Repair in the UK says he's, "heard the same story here" (in the UK). And in Australia, Ben Duffy of Geelong Microsoldering is predicting that micro-solderers like us will see a bump in Tristar failure when, "fake lighting headphones flood the market" - referencing the rumor that Apple is removing the standard 1/8" headphone jack in favor of a lightning port headphone and China's penchant for counterfeiting popular consumer goods.
In short, unless Apple has produced, or authorized the production of lightning port accessories, no matter the attraction, you put your device at risk by using them.