I'm very sorry this happened to you. The seller is definitely a scammer. There is no way that the eggs would "accidentally" hatch prior to shipment or during shipping. That is a complete lie.
I raise chickens, quail, and ducks. Unlike parrots, these birds have precocious young that do not require hand-feeding, so they can be successfully raised in a brooder without special training. Baby chickens are MUCH easier to keep alive than a baby parrot.
I have purchased fertile eggs for poultry breeds that are difficult to find in my area. The eggs are gathered shortly after being laid by the hen and BEFORE incubation begins. This is very important, because once the eggs have begun incubation, their requirements change dramatically. Before incubation, the egg is in a kind of stasis, like a seed, waiting for water. They can still be harmed by exposure to extreme temperatures or too much vibration during transport, but so long as care is taken with the package, the freshly laid, fertilized eggs can be safely transported without special equipment. If you try to transport incubating eggs, then you much maintain a steady incubation temperature of 99.5 degrees Fahrenheit, as well as keeping the humidity correct AND turning the eggs regularly. They would not survive a three day trip in the mail. They would not even survive a one day trip. Fertilized chicken eggs MUST be unincubated to be successfully shipped. The person buying the eggs will put them into an incubator after the eggs arrive at their destination and start the incubation process. It can't be interrupted after incubation begins or the eggs will not hatch.
However, timing is very important. The longer you wait between the time the egg was laid and the time when incubation begins, the fewer eggs will successfully hatch. To have a good hatch rate, you should try to minimize this time as much as possible, by gathering freshly laid eggs, expedited shipping, and starting incubation as soon as the eggs are received. For chickens, you have about a week to start incubation from the time the egg was laid. Longer delays will significantly lower your hatch rate. Most chicken breeders will have multiple hens, so they can gather many eggs in one day and ship a dozen eggs out all at once. The extra eggs are important, because you can expect that out of a dozen eggs, you will have some that will not hatch, for one reason or another, so when you are hatching chickens from eggs, you generally plan on buying more eggs than you need, to make up for expected losses.
For chickens, the incubation process takes roughly 21 days to complete. So the seller would gather freshly laid eggs, ship them out the same or next day, the buyer would receive the eggs within a few days and get them into an incubator. In about three weeks, the eggs would hatch and they would have brand new chickens ... assuming that everything when right during shipping and they were incubated at the appropriate temperature and humidity.
Now think about this process in relationship to parrots. They will lay an egg every other day and start incubating their eggs immediately. Unless you had a large flock of parrots that were all laying at the same time (like you would have with chickens), it would be nearly impossible to gather a dozen freshly laid parrot eggs to ship out at the same time. At best, you might be able to get three or four eggs at once if you had several breeding pairs laying at the same time. You would need to pull the eggs soon after laying and get them shipped as quickly as possible. The buyer would need to start incubation as soon as the eggs arrived and some of them would not hatch, so they might end up with one or two surviving chicks. These chicks would then need to hand-feed from the moment they hatch and require 24 hour intensive care to keep them alive. Even experienced breeders lose chicks due to the challenges of hand-feeding. Someone who has never raised a parrot chick before is very likely to make mistakes and those mistakes could easily cost the life of one or all of their chicks. It is a recipe for disaster. Unless all you care about is getting a quick buck by selling parrot eggs to unsuspecting people. And in that case, you don't even need to own a parrot. You just need to convince them to send you some money.
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Long story short, there is no way that the eggs could hatch prematurely if the seller was making any real effort to get fertilized eggs to you in a reasonable way. As tka said, this is definitely a scam. The parrot eggs never existed in the first place and they have been lying to you from the start.