Malignant melanomas can occur at any age, the other main types of skin cancer (Squamous cell or SCC and Basal cell or BCC) are much more common in people over 50.
The people who would have had most sun exposure (farmers, field workers, navvies, construction workers etc) were also the ones less likely to reach old age because of their social circumstances.
So it’s partly that people are living longer, and partly that people were exposing more skin to the sun.
My grandmother lived in Southern Africa (South Africa, Zambia and Zimbabwe) for more than 60 years. She had an SCC removed from her face aged 70, and by no means was the only person of her acquaintance to be affected. Many caucasian Australians over 60 have also had an SCC or BCC removed.
Having dark skin isn’t a complete protection from the sun. A Kenyan friend or mine went back on a visit after some years away and still got sunburned. It is believed that Bob Marley died from the brain metastases originating in a malignant melanoma on his toe. No matter how dark your skin is, you should still wear sunscreen (albeit of a lower factor) and take precautions in the sun.