That language may be misleading you – the mentions timeline is just about mentions of you, not retweets of your tweets. The only retweets that would potentially ever surface in a mentions timeline are retweets where your account was mentioned in the originating tweet.
The website uses a timeline that is different than the mentions timeline. That timeline is not available in the public API.
Until statuses/retweets_of_me potentially makes its way to API v1.1 (it’s part of API v1), the best way to accomplish this is looping through your own user timeline and using statuses/retweets for each tweet with a non-zero retweet_count.
statuses/retweets_of_me isn’t the same as what you see in the interactions tab either, but it is a simplified short cut to the process I outline above.