If I enable the "Message Posting Doublepost Options" checking on my dev site (with "Timestamp Update" set to "Yes"), and then use of of my dummy accounts to double post, here is the post:
Note the timestamp of 11:41 pm.
Now, when I go to the Forum Display page for the forum containing the thread which contains the above post, I see:
And then when I go to the home page, I see:
Note that the timestamp has been correctly updated in all 3 places.
Can you provide similar screenshots so we can see what happens on your forum?