Will say this again and will bold it and underline it:
Node execution within a workflow, a sequence of nodes execution, is synchronous.
If there is an issue in a scenario where there is a raise new request node followed by an update the newly raised request, if the update does not happen, this is NOT because node execution order (e.g. because of asynchronous execution, this is not the case, the nodes execute synchronously). This can potentially be a caching issue, but is something that should be working, but it isn't, so something Hornbill needs to investigate and address.
EDIT: the scenario where once a new request is raised, which has it's own workflow running, between the "old" request and "new" request, if both have running workflows, they will execute asynchronously because, in essence, they are different workfows so they will run asynchronously... so one would need to be aware of this apsect when designing the workflows for the "old" and "new" request.