The main reason for JINN to be ternary, is that it is based on development of a ternary general purpose processor. I have searched alot on this topic, but the only conclusion I can draw is that they don't want to give up on the ternary idea, or because they think it is cool, but not because of performance reasons.
In the ideal theoretical case, when only looking at storage, and not a practical limitations, using a ternary system is about 6% more efficient than a binary system (https://en.wikipedia.org/wiki/Radix_economy).
Even for systems where efficiency is important (which IoT is, but also in smartphones for example), a 6% improvement on CPU efficiency is not really all that impressive, certainly not a reason to switch to a completely new architecture. The efficiency improvements and tricks current manufacturers have in their designs will be alot more than 6%, and in addition there is the question how efficient the compiler will be compared to the well established and optimized compilers which exist for for example ARM.
In addition that is assuming you completely use all bits/trits. For example, most IoT stuff will probably run at 32-bit processors (depending on your definition of IoT). Which allows for integers between 0 and about 4 billion. While if your program only uses integers between 0 and 1 billion, you could do with a 30-bit CPU instead of a 32-bit CPU, which is also about a 7% boost in efficiency. No one is obviously ever going to do that in practise.
So I cannot find any proper advantages of ternary for their use case (the links to Neural Networks in other answers are interesting, but also a completely different use case). Not to mention I would first switch away from Java if you want to run it efficiently on IoT ;).
But why not do it ternary? Besides that if you would just do it binary it would be more efficient on existing binary hardware, which are way more optimized by manufacturers than 6%, there are a ton of issues with making ternary logical gates. I am not aware of any method to make them efficiently. I believe the latest information is they are using a tripple rail setup, which is better than some others ideas I have seen, but still I cannot see how it will come anywhere near binary logic gate performance.