Alright so a Rabbi will come into your facility and do the following based on my experiences:
1. Inspect your product labels. They will see the ingredients list, and make sure you are using the correct logo, for example if its Pareve or Dairy..etc.
2. The products you have certified as kosher have certain processes you do to maintain their kosher status. The Rabbi will inspect these processes and make sure you are following the correct measures according to Kosher. For example, are you sharing equipment with non-kosher? If yes, how are you cleaning these equipment? Are you mixing dairy with meat?
Let me give you an example of an inspection we had:
We did roasting of nuts. So nuts are naturally Pareve, but they needed to see what type of oil you are roasting it in, I had to get one that's kosher AND make sure it came with a kosher cert to prove.
Once we did the nuts, we used butter in some to make toffee nuts. So butter is dairy. they needed to make sure the product is labeled as Kosher Dairy. If you are then proceeding to a non kosher dairy product using the SAME equipment, they needed to see how you are cleaning it. Or how you are managing your production to ensure that you do non dairy then dairy. Also for example the way you transfer the oil you purchase into your tanks ALSO needed to be kosher (very odd, you were not allowed to transfer it to another tank unless a rabbi approves it), so we just used the original big totes they came in to eliminate that transfer process. Also after we roast some nuts, we seasoned them, and when you season them you add oil and this oil has to be cooled down before adding it (very odd). Also make sure your seasonings were kosher.
Also, they don't really care if you're SQF. or any GFSI. They just come in and make sure you are in fact following kosher guidelines. There are many documents online you can go through that can explain what to do and what not to do depending on your processes.
In your case since everything is dairy, you need to make sure you labeling Kosher Dairy, and they would wanna see your processes.
Some Rabbis are really nice and they would take the time to explain everything to you if there is something you are not familiar with. They are very lenient as well. (Some).
I hope that helps :)