No, fermentation didn't start again,
your airlock started venting co2 again.
That is not the same thing. You have to seperate the idea that aircock bubbling and fermentation are
two seperate things.
Your airlock is NOT a fermentaition gauge, it is a VENT for Co2. When you closed up the system you tightened up the lid and again began to void co2 out the airlock, along with any AIR you got into it while it was opened.
airlock bubbling, lack of airlock bubbling, stopped airlock bubbling, fast airlock bubbling, slow airlcok bubbling, heavy metal airlcok bubbling, or disco airlock bubbling really is not an indicator of what is happening to your beer, really isn't important, and it is NOT an accurate gauge of fermentation.
If your airlock was bubbling and stopped---It doesn't mean fermentation has stopped.
If you airlock isn't bubbling, it doesn't mean your fermentation hasn't started....
If airloc starts bubbling again, it doesn't mean you fermentation has started again.
An airlock is a vent for excess co2, nothing more, it's to keep your beer off the ceiling, and is designed to vent and still keep stuff out of your beer....that's really it...
In fact many no longer use airlocks at all, just cover the hole with a piece of tinfoil, or use a piece of plexiglass instead of a lid.
You did right by using your hydrometer,
which is an accurate gauge of fermentation. But get away from thinking your airlock means anything other that something to let excess gas out and keep bugs it, and you will be much happier......
If you want to read about how faulty an airlock is, read this
https://www.homebrewtalk.com/1156967-post6.html
Oh and you don't have to rush you beer...just becasue it has reached FG...you will find your beer is much better if you do what many of us do and leave our beers in primary for 3-4 weeks, to allow the yeast to clean up after themselves.
Just becasue it is done "fermenting" doesn't mean that the yeast is done doing their job. They are very fastiduous creatures who like to clean up the mess they make during fermentation...the stuff that if you rack too soon can lead to off flavors. That's why a lot of us don't secondary and instead leave our beers alone for 3-4 weeks, then bottle...and only secondary if we are dry hopping, adding fruit, or oak. And even then we usually wait 10-14 days before moving our beer.
So don't be in a rush, this is a patience game, and your patience will be rewarded with great beer.
In fact even John Palmer mentions the benefit of not moving the beer right away.
From How To Brew;
Leaving an ale beer in the primary fermentor for a total of 2-3 weeks (instead of just the one week most canned kits recommend), will provide time for the conditioning reactions and improve the beer. This extra time will also let more sediment settle out before bottling, resulting in a clearer beer and easier pouring. And, three weeks in the primary fermentor is usually not enough time for off-flavors to occur.