Concepts
Async in ATARC
The meaning of "Async" for ATARC is pretty much related to queueable executions. Salesforce provides queueable classes which you can execute and forget, Salesforce will take care of executing it whenever it has resources for it.
It is a very powerful feature as it helps you make room in your current transaction context while code is running in the background which doesn't require provide any feedback to the user.
When an Atarc Process has been upgraded to Async (has "IsAsync" flag enabled) it basically upgrade itself to a queuable class thus will run in a seperate transaction context not in the same as originated the execution.
So, in simple words, upgrading an Atarc Process to Async is just referring to the Atarc Process's code running as a queueable.
It is possible to execute an Atarc Process using Async mode, then waiting for it to finish before executing another Atarc Process in Async mode as well, this is called Async Chaining.
Async Chaining, its possible when the first Atarc Process does not have Isolate flag checked.