Spring is unfortunately (along with Autumn) the rainy season in Fethiye.
Some flowers bloom earlier than others, so depending on when you go, you may see a variety of different flowers. April and May tend to be the recommended months as they have slightly less rain than March, and you can usually guarantee that by then the flowers will be out, however the later you leave it, the slightly increased chance of summer arriving early and the blossoms vanishing.
However, a solid review of the tulips and flowers showed them in early March. So to some extent it's a bit of a luck of the draw.
Basically, the later you go, the better chance of good weather, but the slightly less chance of seeing flowers.
To go for the best 'chance' of both, I guess that would average out to be early April then.