The simple way to think about it is the pool will confirm the payouts with the future blocks that the pool finds. Basically, when new blocks are found, those blocks are used to confirm the payouts for previously found blocks.
Technically, this is because as Kano was saying they are free transactions so no one else will confirm them. However, they are the pools transactions, so the pool will confirm them. The pool will do this whenever it finds a new block.
There are a few *'s to the above with blocks needing 100 confirmations before being spent, dust transactions (I assume your first few payments are dust as your 5N ramps up and this isn't a huge issue), etc, but the above will get you close to answering your question quickly and somewhat painlessly
If all else fails, just watch the payments come in and after awhile I am sure the pattern will make sense with a little more exposure to it.
This is probably the clearest...FWIW, I've been running six S3s for quite a while...only have three running right now due to power limits, and an A6 is taking up the slack on the home front (I have three S7s in a data center). At today's pool rate, and today's spot, you're looking at maybe 0.00019037 per block, or USD$0.118. I keep my S3s for backups...using three right now to try to make up for a downed A6. They would not be profitable to run except that I have free power here. S3s can vary widely in how well they handle clocking. I'm able to overclock five of mine to 250 without issues, but one of them won't run over 237 without getting x's. Overclocking, btw, will only get you another 50gh or so. If you're not so concerned about revenue, don't do it. It isn't worth it, and just takes up more power, and unless you monitor your machine closely, you could harm it.
If you're running your S3 essentially for learning, cool. Good way. You won't, however, get any payments as Kano doesn't pay dust. BTW...don't feel bad. I'm a certified genius (200+IQ) with 50+ yrs in IT and finance, and I still don't totally "get it" sometimes. I often joke that my IQ and USD$2 gets me a cold beer at the beach food truck down the road.
This is a decent bunch of folks here, and they will help you as best they can when they can. Some of us can be a bit blunt sometimes, but it's a dynamic business and it tends to get that way (blunt) sometimes. Don't take it personally.
Welcome.
Keep calm. Mine on.