We have a couple of Trachelospermum jasminoides here in the UK (flowering with delicious fragrance at the moment), and one much bigger in Greece. We have never had seed from the ones here, though we have had seed in Greece. I'd always assumed it was insufficient warmth here, as Herklots (Flowering Tropical Climbers, Dawson, 1976) says "It is disseminated widely by seed." I have seen hawk moths hovering around ours in Greece, and believe they are common pollinators for it; do you have those, Chantal?
Though this is almost always seen as a climber, it does also make quite an attractive low sprawling shrub.