Is there a term for the type of communication where the feedback is immediate, as opposed to delayed?

In pedagogical terms, we talk about "synchronous" vs. "asyncronous" communication.

In synchronous communication, we're talking to each other at the same time; in asynchronous communication, you may not see what I'm saying as I'm saying it, and you may reply at a later time.

Good question. In some ways, you are suggesting "active feedback" rather than passive, though that is not a common term and it doesn't mean "asap".

Tech companies I have worked for also discuss a "positive handoff" which means reaching out to the person actively, such as via phone (I just emailed you the report) or in person (Here is the report) as opposed to a passive medium like email or a phone message. This is used for accountability purposes (I had a positive handoff of the contract with client X on 1/1/11, so he can't say he didn't know it was finished...)