Should postdocs work only on the projects they are hired for, or can they work with other people in the same research group on other projects?
Since the supervisor got the grant, he is ultimately responsible to the funding agency for the research that was funded and for any results. So the postdoc should definitely talk to the supervisor.

Actually, this would be a great opportunity for the supervisor to help the postdoc grow academically, since postdocs are of course expected to take on more responsibilities than Ph.D. students, and start making their own reputation in a field, not stay in the supervisor's shadow. So the supervisor should certainly understand that the postdoc will start flexing his wings and be interested in other topics - it just needs to be commensurate with the goals that the supervisor got the money for.

If, conversely, the postdoc got his own grant, he should first of all look through the paperwork he presumably got, signed and returned before the money started rolling in. It is quite possible that an expectation of the funding agency as to the amount of work the postdoc should be spending on this particular project is already somewhere in the paperwork. Of course, even in this case, it makes a lot of sense to discuss this with the supervisor, who presumably has a lot of experience in this field, and possibly with this particular funding agency.