Greetings Leia. The Taino Resurgence Movement is a complicated phenomenon (as is pretty much anything that is powered by so many personalities). In general I want to assure you that there are certain consistent assumptions that tend to remain steady across the majority of groups and individuals who typically form part of the movement. These (and of course there will always be exceptions) are as follows:
1.) The vast majority of those who identify as Tainos agree that we are Indigenous to the Caribbean islands, that we are the original people who have lived in that geographic region.
2.) The vast majority of us accept the fact that our people belong to an ethnic group that is part of an Indigenous language family known as the "Arawakans". This language family gets its name from one of its many member tribes the Arawaks (Lokono).
3.)Many (but not all) of us belong to organizations that identify as communities normally known as "yukayekes". The word "yukayeke" is a term taken from the Taino language and denotes a place where people live such as a village. Members of a yukayeke don't have to all live in the same geographic location. They may be associated to each other online, and a huge number of us are diaspora Tainos who don't currently live on any of the Caribbean islands but in countries such as the mainland United States and Canada.
4.) The Taino Resurgence Movement began around 1992 when a number of individuals of Caribbean ancestry who had always felt drawn to Indigenous culture reacted to the world-wide celebration of the Columbus Quincentennial and began to identify as Taino and to form into formal organizations with names. One of the first of these organizations was the TAINO NATIVE AMERICAN ASSOCIATION in New York City, which eventually evolved into the modern-day Maisiti Yukayeke Taino. The members of these organizations meet on a regular basis. They hold group celebrations and ceremonies, and seek to maintain Taino identity and group cohesion. Many people who have been participating in the Taino Resurgence Movement identified as Taino long before 1992 but there was never an organized, consistent and purposeful movement as what began in 1992. Of those who identify as Caribbean Indigenous there are a few communities who actually are remnants of the original people who maintained their identity intact since ancient times. These communities include the so-called "Indieras" of Boriken (Puerto Rico), the "Caridad De Los Indios" community of Baracoa, Cuba and the Kalinago (Carib) reservation on the island of Dominica in the Lesser Antilles. Some members of these original communities participate in the current Resurgence movement, hoever the vast majority of those who participate in the movement are recent "reawakened" who have arrived at their Taino self-identification within the past thirty years.
5.) An important element of the Taino Resurgence Movement is spirituality. Inspired by the power and energy that traditional Indigenous spirituality provides to the vitality of other Native communities of the Americas, many modern Tainos have turned to the ancient spiritual tradition of our ancestors to support our claim to our identity. This is not always an easy task. Our people were profoundly colonized in both body and mind. Our original tribal spirituality was violently crushed by the invaders. Most of our people have followed Christian spiritual traditions for generations after the conquest, and many modern-day people who claim Taino identity still cling to Christianity as their main practice, even those still living in the original surviving communities such as Caridad De Los Indios of Cuba and the Carib Reservation of Dominica. But the majority of those who participate in the Resurgence movement have turned their backs on Christianity and embraced whatever they can recover of the ancient traditions. I personally belong to a Resurgence movement group called CANEY INDIGENOUS SPIRITUAL CIRCLE. Others follow their own interpretations of whatever original spiritual tradition we have been able to recover.
I hope this information is of use to you. Please don't hesitate to reach out to me if you wish more information.