There's the math, there's the emotions, and then there's the decisions. The timeline of each can be different.
Usually the math comes first. For me, I hit my number on June 20, 2015, when my FIRE stash supported a 95% success rate at my Quicken-measured spending level.
For me the decisions came next. I ran my numbers through more torture, thought about what would happen if the market dropped, etc. I went on sabbatical in November 2015 and officially RE'd February 19, 2016.
Emotionally coming to grips with everything is a process: "Am I really there? Do I deserve it? What will other people think? Does it feel safe?" I think most people process some or all of the emotional aspects before deciding to RE. I had been looking at FIRE and planning for it for probably fifteen years, so I had worked through much of the emotions over that time frame. Still, there was emotional processing after RE for me, which I think is just stuff you can't grok until you get there and actually do it.
As a direct answer to your question, I was watching and updating my numbers daily, and declared victory the first day the numbers hit the mathematical mark. If they had dropped below that number the next day or the next month, I still would have retired based on my temporary achievement; I would not have worked longer just to get the number back up. My thought was that those fluctuations were covered by the 4% rule. However, I can see other people choosing to do otherwise depending on their personal preferences and situation and goals. (Fortunately, I retired into a rising market, so my numbers have not yet dropped below that June 2015 data point.)
I'll add that in practice, once you get close to the FI point, it really becomes a little mushy and you can rationalize your way over or under the line by counting or not counting assets, income, or expenses. This behavior can easily delay or accelerate your FI date by a few years.
