Here is a link to a page that has a copy of King's tweet: http://whotv.com/2016/02/02/steve-king-tweets-under-fire-by-ben-carsons-campaign/
I'm not sure what you will see for the time stamp, because I think it will translate the time stamp to your local time (I see 8:20PM since I am in the Eastern time zone). However, if you hover over the time stamp, you will see that the tweet was made at 01:20:52 UTC, where UTC is universal (Greenwich) time. Since Iowa is in the UTC-6 time zone during the winter, this conclusively shows the actual time of the tweet was 7:20 PM Iowa time, not 8:20 PM (which Rove probably saw when looking at this tweet from Washington DC).
The other times in Rove's analysis were in Iowa time; the refutation by Carson was 40 minutes AFTER King's tweet, not before. So this pretty much nukes Rove's entire argument.
Interesting. Thank you.