Mainstream processors are synchronous. For this reason there is a global clock needed to synchronise all (most) the chip parts.
I remember there was some research on asynchronous CPUs but I don't think it ever yielded anything commercial.
What you are saying is that they react to interrupts asynchronously, but this has nothing to do with the synchronous nature of a CPU.
Moreover I think that if you have a CPU that doesn't respect the barriers and reorders the instructions to execute them in parallel, then it's a bugged CPU.
EDIT: Wikipedia link: https://en.m.wikipedia.org/wiki/Asynchronous_circuit
What you are saying is that they react to interrupts asynchronously, but this has nothing to do with the synchronous nature of a CPU. Moreover I think that if you have a CPU that doesn't respect the barriers and reorders the instructions to execute them in parallel, then it's a bugged CPU.