First time egg pickler, does pressure in jar mean they're spoiled?
As somebody who ferments things, unexpected ferments generally should not be trusted. Even I throw them out, even though I'm pretty sure they're safe, personally.

Based on these two recipes and others I Googled, it seems like fermentation is not expected or desired. It seems like the two recipes you link to assume that the acidity of the pickling brine will be enough to preserve the eggs at room temperature for some time. We store vinegar at room temperature all the time!

But there are a lot of variables that could affect this. How much sugar did you use? How much chili and garlic? were they fresh or dried? How big were your eggs, and how much vinegar did you use relative to everything else? How much water did you add to your brine mixture before simmering it? And how long did you let your brine cool? 

Although sterilization is hugely important, so is the pH of the brine and salinity/sugar content of your additions. So if you're inventing recipes, make sure you take some time and really think through how your additions could be altering the pH of the overall solution. If you're lowering it, consider how that might change the method.

In order to keep this from happening again, I would recommend hot-packing your eggs, and consider looking into canning them. Hot-packing means take your jars out if the oven, put your eggs in them, pour in your hot brine, and close the lid. Then let them cool and transfer to the fridge.