By the end of the movie, there are no promises that Toomes isn’t going to start telling everybody he can about the secret, but the mid-credits scene provides confidence that he will be keeping it to himself.
This is the wonderful benefit of keeping Toomes alive at the end of the film and not just killing him off!
Of course, on some level Adrian Toomes really had to refuse the offer for the betterment of the franchise.
Spider-Man: Homecoming makes the bold decision to have the Vulture discover that Peter Parker is Spider-Man, and considering how few people have that information in the comics, that’s a pretty big deal.