Hi Shannon,

Thanks for the message. This sounds like a very interesting and flavorful recipe. I haven't made nor analyzed this recipe before, so my feedback is based on some assumptions. 

The first portion of the recipe is essentially holding the spices in a high acid solution (lime juice). Due to the pH, this is unlikely to be a fermentation, but instead just a high acid soak to support flavor extraction and uniformity of the flavor in the mixture. 
The second section is an addition of more acid and oil and some low acid ingredients which is stored at room temperature. Again, unlikely to support fermentation due to the likely very low pH, so more of a flavoring situation. 

This recipe generally doesn't match to our recommendations for acidified foods as it doesn't include any thermal processing and we generally discourage the use of oil (there are some specific exceptions). The pH of the mixtures has not been measured (or is not provided), so I can't be certain of the safety of the product. Without any thermal processing and air in the top of the jar, it is possible that the product will develop mold or yeast on top, so watch for those signs.  

Sorry to not be able to provide more clarity, but these are my thoughts on the recipe.

Thanks for using Ask Extension.
Joy

Thank you so much Joy for the thoughtful answer. Next time I try the recipe, if I were to store it in the fridge throughout the whole process, would that ensure food safety? 

Hi Shannon,
Storage in the refrigerator is a good idea, but it will likely take longer to get full flavor development. 
Best of luck!
Joy