Is cancer hereditary if your parent developed a tumour after I was born?

Unrelated. Hereditary cancers can develop at any age. Therefore, your parent's age of onset of cancer has no relationship with this. There are blood tests available to check for certain hereditary cancers--check with your parent's oncologist to see if this is appropriate for them.
Maybe. Some cancers show a mild hereditary tendency, and there are several dozen genetic diseases passed from one parent to children with 50% odds that make cancer likely. Your physician knows brca1&2, men1&2, the polyposis and hereditary pancreatic cancer syndromes. However, the vast majority of both adult & childhood cancers strike at random; limit your clear risk factors & accept normal screening.