Don't know about the discoloration, it probably will fade over time, but I doubt that your eyes will ever be able to not see it without some intervention.
Others around are much more knowledgeable than me, but...
- I don't think Pebble Tec brand has a color called "tropics blue", they have a tropical breeze, possibly semantics, but it leads me to wonder if this is truly pebble tec at all.
- There looks to be way too much plaster in your photo... meaning not enough pebbles. Did they acid wash it?
- With the plaster, it looks like 50/50 pebble to plaster... a good install should be 80/20 or 90/10ish in my opinion... If I am correct, and that's a big if... this finish likely won't last as long as a proper pebble finish should.
Sorry that you're having to deal with this, I hope that my observations are off base and someone else give you some better direction. To my untrained eye, something looks "off" with that finish. I personally don't think there is anything wrong with a knock-off pebble finish, but if they contracted with you for pebble tec, it should have been installed by a certified pebble tec contractor. If they "forgot" to do the startup, is it possible that they also "forgot" the acid wash? It honestly could be the same as your sample, but if the excess plaster isn't etched out, it won't show the pebbles properly.
If it were mine, I would ask them how they intend to fix it. Don't start with demands, see what they say. I would expect a redo of it quite honestly. Do you mind sharing where you are in FL? In the Orlando Area, I think there is one large Pebble Tec applicator for instance. If it is indeed a pebble tec product and applicator, you could possibly reach out to pebble tec directly and get them to put some pressure on the applicator to fix it.