Worm eggs are hard to kill in the soil. They can survive for years in the soil, including frozen ground. Only fire or steam can eliminate them.
Some insects can be vectors for some types of roundworms and all tapeworms. Treating the soil to eliminate insects is fine, provided your birds are penned.
I rarely recommend putting wormers in water for birds to drink. There's no guarantee that birds will drink the treated water, or drink enough of the treated water to be effective, sick wormy birds rarely drink at all. Direct oral dosing is best, that way you know they properly wormed. No guesswork about it.