The API is what connects the TCP hub and the Wink hub.
If you issue a command in wink to turn of a TCP bulb, the following happens:
-The command moves from the Wink app to the Wink hub to the Wink API
-The Wink API then send the command to the TCP API
-The TCP API then sends the command to the TCP hub then to the TCP bulb.
The API is basically the online server that can communicate with partnering companies APIs. Once they shut down thier API the chain will be broken. There is nothing Wink, SmartThings, Vera or any other HA controller can do about it.
This is new technology and most consumers are unaware how useless some products are once the company drops support.
Just look at what happened when Nest "Google" bought Revolv and then ended support.
http://www.theverge.com/2016/4/4/11362928/google-nest-revolv-shutdown-smart-home-products