The Dutch midfielder played just 11 times last season, eventually moving to Crystal Palace on loan in a bid to get games.
Agustien arrived at Swansea on a free transfer with an injury which Rodgers says hampered his chances of getting into the team.
But now fully fit, Agustien will have a fresh chance to impress, the Swans boss describing it as a 'new start'.
Rodgers said: "I spoke to Kemy and think his career at Swansea didn’t get off to the best start simply because he came in injured and with the team starting so well it was very difficult for him to get into the team.
"He understood that but he was frustrated and he will tell you that.
"He’s a good guy and I wanted him to get games and he did that towards the end of the season at Palace, which showed he has got a run of games in him.
"I told him this is a new start and he has looked good and did well in a short period at Neath."