I think those plants will make it just fine. They are going to look very different tomorrow when it dries up a bit, I think. Can't tell what they are, but that one in the top part of the photo looks like a shrub of some sort? I'm thinking the rain is going to be more beneficial than harmful. Don't go tromping around in that bed while it's wet for a day or two. It might pack the soil and cause issues later. When the plants get established with larger root systems, they'll use water a lot faster and you may not see it puddling like it is now. Just takes time to get things balanced out.
