The family had asked that half the remains be returned to them with the other half scattered in the grounds.
Half were returned but the remainder had been wrongly used in an un-witnessed scattering earlier that day at  Weston Crematorium, Worle.
The two workers lost their jobs and Dignity, which runs the crematorium, apologised for the family's distress.
Instead of admitting their mistake, two members of staff, who have been described as "very experienced", tried to cover it up by using another person's ashes for the ceremony in front of the family.
Eventually, they admitted what they had done to their manager, and Dignity - which runs the crematorium on behalf of North Somerset Council - started an "extensive" disciplinary hearing.
In a statement Dignity said it was an "isolated incident" and would look at why "very experienced staff failed to follow our established procedures".
"Following disciplinary hearings, two employees are no longer in our employment. The family and North Somerset Council have been kept fully informed throughout."
A North Somerset Council spokesman said Dignity had kept it "fully informed during the process".
"We are satisfied that they have investigated the matter thoroughly."
The ashes of a stranger were scattered in front of a family by two cemetery workers trying to cover up a mistake.