The way you’ve described it doesn’t sound like it’s a current feature of the review queue. 
You generally see the view full conversation option on flags that also create a PM to the moderators group (the ‘something else’ and ‘illegal’ flag types). Pressing that will take you to the PM itself rather than the reviewable in the queue.
There’s no time delay on when that option becomes visible, it should be there immediately on the flag landing in the queue. And the spam, off-topic, and inappropriate flags don’t have that button at all (as they don’t generate a PM with extra detail in).
Does that match up with what you’re seeing in your Review Queue?