Surviving ancient sources are scarce and often unreliable, we do not know and will never know who was "first". Aristarchus's is the earliest heliocentric proposal we have solid evidence for, Seleucus possibly supported it a century later. The partially heliocentric proposals reported by Adrastus and Theon for the inner planets (Mercury and Venus) also postdate Aristarchus and even Hipparchus, see Keyser, Heliocentrism in or out of Heraclides.
In the older history books it was suggested that Heraclides and Ecphantus had the inner planets circle the Sun. The meme dates back to the end of 19th century when Schiaparelli, the discoverer of Martian "channels", promoted it. That is not full heliocentrism, and even that is not supported by modern scholarship. The Wikipedia article linked in the OP quotes Eastwood's Heraclides and Heliocentrism to that effect a few lines down. Here is a fuller Eastwood's quote:
"Only two sources have ever been cited to support the connection of Heraclides's name with a heliocentrical motion. These are Simplicius's commentary on Aristotle's Physics and Calcidius's commentary on Plato's Timaeus. I deal below with both, the first more briefly, the second in full detail... What I propose to show is that Calcidius's commentary (and incidentally Simplicius's work as well) offers no ground whatever for attributing to Heraclides of Pontus
an idea of circumsolar orbits for Mercury and Venus. This idea came into the Middle Ages only through Martianus Capella.
Nowhere in the ancient literature mentioning Heraclides of Pontus is there a clear reference to his support for any kind of heliocentrical planetary motion. Even more to the point, in none of the places where we find Heraclides's well
known proposal of the hypothesis of Earth's diurnal rotation do we find any suggestion of some further revolutionary idea such as heliocentric motion for any of the planets. The conclusion should be clear - modern proposals for an
ancient Heraclidean heliocentrism have come from post-Copernican expectations rather than from a dispassionate reading of the texts."
However, there were older Pythagorean models that we know of where the Earth was moving... but not around the Sun, see Danezis et al., From Pythagoreans to Kepler. In the model of Philolaus they both moved around the "central fire", a.k.a. the "hearth of the universe". Hicetas had an even stranger idea, as reported by Cicero:
"The Syracusan Hicetas, as Theophrastus asserts, holds the view that the heaven, the Sun, the
Moon, the stars, and in short all the things on high are stationery, and that nothing in the world
is in motion except the Earth, which by revolving and twisting round its axis with extreme
velocity produces all the same result as would be produced if the Earth were stationery and the
heavens in motion"
Some historians believe that Pythagorean models influenced Aristarchus.