API
There is no public API yet. This page says so plainly rather than showing documentation for something you cannot use.
What exists today
Vibileo talks to its own server over addresses that are tied to your browser session and protected against requests from other sites. They are part of the application, not an interface for other programs, and they change whenever the product changes.
What is planned
API access is named in the Enterprise plan on the front page. It is not built yet. When it is, the reference will be on this page — with keys, addresses and limits.
If you need it now
Tell us what you would do with it. What people actually need decides what gets built first.