According to the Valmiki Ramayana, during his exile in Dandakaranya, Rama met the Sage Agastya (Aranyakanda, Section 11). On his way to his asylum, Rama said the following thing to his brother Lakshmana.
The righteous Agastya it is who, wishing for the welfare of the worlds, destroying by virtue of his austerities a Daitya resembling Death, hath rendered this quarter habitable. - Ramayana 3.11.54 (verse number is from Gita Press English Ed.)
He was talking about the land south of the Vindhya mountain. This will be clear from the following description. After narrating Agastya's deeds (Killing the Rakshasa Vatapi and Ilvala), Rama said -
This is the asylum of that pious one, who destroying (the Asura resembling) Death, hath, desirous of the welfare of mankind, rendered the Southern quarter habitable, and through whose potency the Rākshasas from fear barely cast their eyes in this direction, but do not approach. Ever since that one of pious ways possessed himself of this quarter, the rangers of the night have foregone their hostility, and assumed a peaceful attitude. This Southern quarter rendered safe (by Agastya), and incapable of being harassed by those ones of tortuous ways, is celebrated over the three worlds in conection with the name of the reverend ascetic. And this graceful asylum ranged by mild beasts belongs to that long-lived one of renowned achievements— Agastya—in obedience to whose command, the Vindhya mountain—foremost of its kind—which had always obstructed the way of the Sun, doth not increase. - Ramayana 3.11.81-85 (verse numbers are from Gita Press English Ed.)
The repeated mention of the fact that it was Agastya who rendered the southern quarter habitable for the Aryans, it is clear that he was the first who spread the Vedic civilization to the South. If it was already made habitable by Parashurama, then Rama would not have said that Agastya made it habitable.
The Ramayana - Translated into English Prose from the original Sanskrit of Vālmīki by Manmatha Nath Dutt