Transplants can droop without fertilizer overkill, though too much fertilizer can block the uptake of water. If you see browning leaf tips and edges, that would clearly indicate fertilizer burn. Flushing with water helps, but if the plant has a solid root ball, you could lift it at this point without much of a setback. You should do that if you think you used a lot too much fertilizer. There was probably already some fertilizer in the rootball. It's very common for people to poison new plants with plant food. And some organic sources do release some fast nitrogen.

I'm here in zone 10 in So. CA, and the weather has not been very warm, so if your weather is the same, I'd suggest cutting back on the watering for a few days and see if it perks up in the next week or so.

Thanks for your advice! I think I will lift the rootball up; it should be pretty easy since I just planted. Should I just mix the soil up really well? Also, I just checked around the base with my moisture meter and I definitely do not have it too wet, just moist.

If you think you have too much fertilizer, the general recommendation is to flush it out with lots and lots of water. I would leave it alone, because if it's finally getting settled in, moving it will just shock it further. Water, and provide a bit of shade from the hot afternoon sun for a while.

Yes, I said "if you think you applied a lot too much fertilizer." If you used the amount recommended for new plants and over an area at least 18" wide, it is probably OK even if not mixed perfectly evenly. So Holly Springs' advice is good unless you obviously overdosed.

I planted impatience in my east-facing window boxes. They are drooping again today even though they were thoroughly watered yesterday. (It is 95 degree today.)
When I added a few trailers to the boxes the other day I sprinkled time-release fertilizer (tiny white balls) on top of the sphagnum moss because I didn't add fertilizer when I planted the boxes. I put on a lot of fertilizer thinking that it would take time to work its way through the moss and into the soil. Now I think I put on WAY too much and that is the reason they are wilting so badly.
Is there anything I can do now to save my plantings?