Yes. Even if the other driver is clearly at fault and you've contacted his insurance company, you still have a duty to report the accident to your own insurer.
First, your policy may include coverage that applies even though you weren't at fault (such as medical payments or underinsured motorist coverage). Prompt notice is typically a policy condition, and failure to report every accident may jeopardize your coverage later on.
Second, although it may first appear that the other driver's company will be involved in the case, they may refuse to cover the claim for a number of reasons. If this happens, your case may turn out to be an uninsured motorist (UM) claim against your own insurance company, and prompt notification is required.
The short rule: you should report every accident to your insurance company, regardless of fault.