Well, it's not exactly what branch prediction does.
If I understand it correctly, it does some additional writing to registers (?) and to the cache on its own, and it can leak your data even if you clean up everything you wrote explicitly.
Now, did the vendors promise that this would not happen? I doubt it.
> But wait, how is it even considered a processor bug ?
These side channel attacks allow an attacker to read registers from other processes before any context switching has occurred, or independently of any context switching (even if the OS has been written to correctly clear state).
You write data inside the registers, yes, other processes can read these registers.
It always been like this, and is absolutely normal.
It's the responsibility of the operating system to clear the registers if it is switching context.