They are Jamaican nationals at birth by virtue of ancestry, meaning that they are eligible for automatic citizenship as soon as they are born, yes. All they have to do is report (or have a parent report for them) with a Jamaican embassy and prove descent from a Jamaican born individual (parent/grandparent birth certificates do the trick usually). Their automatic status as Jamaican nationals entitled to citizenship via ancestry at birth is written into the Jamaican constitution.
OK thanks that is not at all that different from other countries. I was born here but my father was born in Scotland. I have not had any motivation to pursue a Scottish/EU passport yet I am interested in my Scottish heritage. Canada is a country of immigrants and we certainly have benefitted from this influx over the many years and Jamaican immigrants have been a welcomed addition. We are quite proud. We welcome all individuals who wish to contribute to our society as CDNs yet can still remember their roots. Come to Toronto during what I remember being called Caribbana. Great party. It keeps the country new and renewed. Probably why Mr. Bolt sees Mr. Degrasse as a younger brother. Take care my friend.