Transactions are processed immediately after they are sent to the respective endpoint. As a synchronous response you will receive 200 as HTTP response code.
Real time workflows (workflows that potentially block a transaction) will respond with a 202 in case processing was not possible till a timeout. In that case the processing will eventually be resumed, often within a few seconds.
In any case where processing is delayed or the result of processing changes due to any operational reasons, respective information will be provided via the API callbacks and the results will be shown in the case manager. The exact times of processing can be seen in the audit trail of the respective case.
As also user interactions with a case trigger callbacks, expect callback to a specific request at any time, also weeks after the original processing. Also expect that cases change into a state that is not typical for a workflow (e.g. Users can open months-old, previously not-opened cases).