The only certain way of salvation is through repentance and faith in Christ in this life, and all who are saved can only be saved through Christ. Whether or not God reveals himself right before death to those who have never heard or had minimal exposure to Christianity is something I don't know. So my answer would be between inclusivism and exclusivism.
Even if you are right (and that would still be on the exclusivist side in that a person would need to accept Christ before death to go to Heaven), Christians cannot know that to be the case. Jesus says numerous times (John 3 is one famous example) that the only way to salvation is through him. Combining those two things says that Christians must act to evangelize others for their salvation.
In addition to the "man on the island" (or in a country with no presence of Christianity), another interesting discussion is relating to people who die as young children (including unborn babies). At what age is one considered able to put faith in Christ as a repentance for their sins. I do believe that people who die extremely young go to Heaven, but I don't know how to define an exact cut off point.
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