If your embedded tweet has an image in it, that image shows up at the top of the embedded tweet.
Compare a screen shot of one of my tweets on twitter.com with the embedded version of the tweet here on my site.
On Twitter:

That is one fine looking embed!
As I recall, older versions had the photos below the text. Or maybe I’ve only ever seen photo tweets on other sites via screenshots taken from twitter.com. Either way, I love how the photos are prominently displayed at the top. Can’t you tell?
Here are more options for embedded tweets — allowing you to turn off the conversations, hide the data cards, show related headlines and customize the design and alignment.
UPDATE: The photos moved to the top just a few months ago. I was worried it had been that way for years and I was late to discover the change.