The only reasons you'd need to water flowers when it's raining are 1. You're using a gold watering can to make gold roses or 2. You're watering someone else's flowers for the breed chance boost. Also, while it's raining on your own island, you can use a gold watering can with no durability use!
You never need to water trees or shrubs. You only need to water flowers if you want to breed them. They won't wilt like in other games and during rain you don't need to bother. In fact rain is a huge pain because it screws up everything when it comes to breeding and it rains almost all the time on my island. And I hear many others complain about that to.