"Send as" and "Send on behalf"
If User A has the Send As right to the User B's mailbox and when sending a message he / she enters User B's address into the From field, the message will be considered as coming from User B, therefore rules covering User B will be executed. However, if User A is defined as a Delegate of User B (On behalf of permissions) and when sending a message he / she enters the address of User B into the From field, the message will be considered as coming from User A, and rules covering User A will be executed.
Please note, that Sent Items Update (SIU) feature works only with messages sent using Delegate (On behalf of) permissions. This is because the software always looks for the message to update in the sent items folder of a person who appears the be the sender.
When sending as, user A sends an email but it appears to be sent by user B. However, user B does not have this message in a mailbox. Therefore, the SIU service will not find it and will not update it.
In the case of send on behalf, a message is sent by user A on behalf of user B. The software still sees it properly as sent by user A and will update a mailbox of a user A, as expected.