Susie is right -- It's all guesses at this point. I don't know the real reason for the problems with Dixie's soap anymore than you do. Just making educated guesses.
"...If this is the case that means it didn't reach emulsion when it was being mixed, is that right? It wasn't caused by overheating in the oven? ..."
If it's an emulsion failure, the cause could be either or both of these possibilities. I'll try to explain --
An emulsion is formed between two insoluble materials when one material forms tiny particles or droplets within the other material. Many different types of emulsions can be made, but sticking with soaping, an emulsion is formed when the fats are broken up into small droplets that float within the watery lye solution.
Emulsions can be temporary or stable.
Temporary emulsions will last for a while but quickly separate back into two layers. A temporary emulsion happens when you shake a container of vinaigrette (oil + vinegar) salad dressing. If you don't shake really hard, the ingredients have the annoying habit of separating while you are pouring them onto your salad. In soaping, briefly whisking or stick blending the lye solution and the fats together forms a temporary emulsion. If you stop mixing, the emulsion will separate back out into a fatty layer and a watery lye layer.
A stable emulsion is one that lasts sufficiently long without having to continually mix the ingredients together. Some kind of chemical interaction is needed (as well as mechanical mixing) to make a stable emulsion. If a vinaigrette contains egg or mustard, these ingredients act as a chemical emulsifier to keep the dressing together sufficiently long enough to dress and serve a salad. In soaping, as the soap batter starts to saponify, the newly formed soap particles act as the chemical emulsifier. The new soap keeps the fat and lye solution together sufficiently long enough for the mixture to saponify into a solid loaf of soap.
Emulsion failure can be caused by two general problems.
One is when a person thinks a mixture is at a stable emulsion, but it really isn't. This can happen in soap making when a person stops mixing at the emulsion stage (before obvious trace) but happens to stop mixing just a tiny bit too soon. Or it can happen if a person sees "false trace" when using a recipe high in solid fats. In "false trace", the solid fats have cooled enough to start solidifying and thicken the batter -- just like putting shaved ice into a margarita. This is not an emulsion, but the thickness fools the soaper into ~thinking~ the soap is emulsified. This thickness magically disappears as saponification gets going and the fats warm up enough to melt. (Or the ice in your margarita melts because you're not drinking it fast enough!)
The other way an emulsion can fail is when something happens to a stable emulsion to "break" it. Emulsions can fail if you add ingredients to a finished emulsion. For example, if you are getting to the bottom of a bottle of hand lotion or hair conditioner and add some water to loosen it up and get the last bits out, sometimes the texture of the product will change and can even look a little like a curdled gravy or "broken" egg custard. You have destabilized a once-stable emulsion by adding water.
Heat can destabilize an emulsion. If soap batter becomes too hot early on, before saponification gets going well, the tiny droplets of fat in the stable emulsion can coalesce into larger ones. As the fat droplets get bigger and bigger, they can separate out of the lye solution and start to float on top of the molded soap. Even though the emulsion was stable at lower temperatures, it's obviously not stable at higher temperatures. It's been "broken" by too much heat.
Destabilization of a batch of soap is more likely to happen when one or more of these factors present --
(1) The recipe contains a high % of water (low lye concentration). More water in the batter makes the fat-lye-soap emulsion less stable. (2) The batter is poured into the mold when it is at the point of emulsion or light trace. The thinner the batter when it's poured into the mold, the easier it is for the emulsion to fail. (3) The soap quickly heats up a lot in the mold either by going into a hard, fast gel all on its own or being heated or insulated too much by the soaper. Too much heat too soon in the saponification process increases the chance for a destabilized emulsion.