Heyerdahl wasn’t navigating except in the most general way. He used the prevailing trade winds and ocean currents to travel westward. He wasn’t trying to reach any particular island. He relied on the fact that there were so many islands in his path that he would be likely to pass close to or collide with one by chance. While he demonstrated the proof-of-concept that a balsa raft was durable enough to travel thousands of miles, as has been said, it wasn’t really comparable to the accomplishments of the Polynesians.
Heyerdahl was basically a crackpot (although, like most crackpots, his ideas had a grain of truth). He believed that the first inhabitants of the Pacific Islands, as far west as Samoa and north to Hawaii, had been colonists from South America. The Polynesians came later, via a circuitous route through the North Pacific, after colonizing Northwestern North America.
Archaeological, genetic, and linguistic evidence has demonstrated convincingly that the Polynesians had their ultimate origin in insular Southeast Asia, and perhaps Taiwan. They reached Tahiti and the Marquesas by around 700 AD. After 900 AD they underwent a rapid expansion eventually reaching Hawaii, New Zealand, and Easter Island.
However, there is definite evidence that there were some Precolumbian contacts between Polynesia and South America. Most notable is the sweet potato (Ipomoea batatas), which originated in and was first cultivated in the Americas. It was found to be a staple crop throughout much of the Pacific by the first European explorers. Although the seeds are somewhat salt-tolerant, the words used for the plant are similar in Quechua (spoken in South America) and in Polynesia, suggesting a human role in its dispersal. The plant is most commonly propagated by vine cuttings.
While a drifting raft from South America could have brought the sweet potato to Polynesia, I think it’s much more likely due to a two-way voyage by Polynesians. The South American cultures were not blue-water sailors, and traveled mainly along the coasts. While a long haul, a voyage from Polynesia to South America was comparable to other trips the Polynesians accomplished. There is also more controversial evidence that chickens might have been introduced to South America from Polynesia before they were brought in by the Spanish.
On the other hand, recent genetic work has shown a small component of South American ancestry in the population of Easter Island that predates European contact by hundreds of years, suggesting at least here the contact might have been from the East.
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