The bulk of the hand-drawn animation was done by Richard Williams, but a lot of Disney animators, or future Disney animators were working for him at the time. People like Nik Ranieri (who I noticed worked on the "Buck Cluck" character in "Chicken Little"), Andreas Deja and Eric Goldberg. Also, some additional animation was done by Baer Animation in Los Angeles. It was a company run by Dale and Jane Baer, who had worked for Disney before, and ended up back there years later. Baer did all of the "Toontown" sequences, and most of the exterior scenes, like the "Benny the Cab" chase sequence. Baer also animated about 10 minutes of "The Little Mermaid", and about half of "Mickey's Prince and the Pauper". You wouldn't think Disney would farm out animation to another studio, but it happens.
Notice that two characters who do NOT appear in "Roger" are Felix the Cat and Popeye. From what I understand, the owners of those characters were each offered a mere $5,000 for the use of each one in the film and they didn't feel that that was enough. This is kind of ironic, seeing as just 7 or 8 years earlier, Disney had teamed up with Paramount to make a whole live action movie STARRING Popeye (with Robin Williams), and at that time, guess who was at Paramount! You are correct! Eisner! Funny how it works that way.