What you are describing now matches what I see. It may be that the change is rolling out to various accounts gradually.
Actually, they seem to be using a yo-yo to roll it out. I was seeing what I described above yesterday, but today I see nothing for my one posted transaction at Home (it only shows me about half a dozen transactions total in Home, and on Monday most of those are Pending from the weekend), though for Pending transactions at Home I still do see:
Rewards
You'll be able to see Rewards information for an eligible charge within 5 days of the charge posting to your account. Please check back later.
They need to make it work over at the Statements & Activity tab for everyone too, because for someone who makes lots of purchases quickly, the whole Home tab small list of most recent transactions can be filled with nothing but Pending much of the time, and a transaction might go straight from Pending to only being visible at View All Transactions which moves you to the Statements & Activity tab.