No airlock activity after water being added late

First, you probably don't need to move it to secondary at all, unless you are adding fruit or something else post primary fermentation.

Second, airlock activity is not a good quantitate indicator of fermentation activity.

The fact that you still have a krausen probably (but not necessarily) means attenuation is not done. But the only way to know that for sure is to take hydrometer readings 2-3 days apart. If they are the same and in the ballpark of what you expected, then attenuation is done. At that point it's a good idea to leave the beer in the fermenter for a few more days to allow the yeast to clean up their byproducts and to allow the yeast and other particles to settle out before bottling/kegging.

Kit directions often suck. Yeast can't read. In your case it probably is too soon to move or package, but there's nothing special about 4-6 days. It could be longer.

 

Yeast can't tell the time, either.

 

The yeast doesn't wait for you to add water to the airlock before it starts fermenting. You simply caught the tail end of what might be described as the visibly active phase of fermentation. In my experience, airlock activity typically slows, or even seems to stop, after two or three days, so what you're describing sounds pretty normal. But it's important to note that airlock activity is not a reliable indicator of fermentation status.

Regarding moving the beer to secondary, 4-6 days sounds reasonable. 3 does not. But these are not hard and fast rules. If this is your first batch, I can understand your desire to rush the process, but I would strongly encourage you to be patient.

Personally, I don't see a need for a secondary. I use kegs, so it's not terribly important. I might consider it if I was bottling, but, even then, it's not absolutely necessary, and many skip the process. FWIW, I leave virtually all of my beers in primary for three weeks. This is almost certainly longer than necessary, but, except for the bigger beers, I'm confident it's done by then.

That said, if you're still learning the process, it's probably best to follow the instructions. Shortcuts can come later.

 

Besides what they said, the water is supposed to be in the airlock for a reason - to keep outside air from getting into the fermenter and possibly staling your beer. Once the wort is in ther fermenter, you want to keep as little air as possible from circulating around and getting to it. The stuff that is there when you seal the top is OK - the yeast does need a little bit of oxygen to do thier thing, and anything leeft will be pushed out by the CO2 being produced.

Also, don't even think about transferring to secondary for at least another week, if at all. The yeast are still doing thier thing, even though you may not see any airlock activity. You can transfer (you can physically do anything you want, though it may not be good for your beer) but getting it off the yeast means that there is less of them available to clean up any byproducnd forgive me, but being your first brew, there are certainly plenty of those.
I personally only bother with a secondary when I need to bulk age for a long time - like months - or am putting it on fruit or sour bugs.
For a normal beer, I just leave it be in primary. I check gravity after about 2 1/2 weeks, then again at the 3 week mark. if the two are the same, I bottle.

 

I bottle, and I don't use a secondary unless there's fruit or it's a real high ABV that needs long conditioning etc. While a secondary might give me slightly clearer beer, the extra work, extra chance of infection and oxidation, extra time, and additional cleaning and tying up of equipment aren't worth it. My beers are often quite clear anyway, and even if they're not, I don't care, because they taste fine.

To the OP:

1. Leave your beer in primary. Don't bother with the secondary.
2. Don't even mess with it for about two weeks. Nowadays I am NEVER opening any batch of beer for at least two weeks. At that point you can do successive wine thief samplings / hydrometer readings to ensure you've reached your final gravity. I realize that waiting is hard, but your beers will come out better if you give them the time they need to ferment, condition, and clear. Patience is a virtue when it comes to making beer!
3. You said "added water" to the airlock. Always add properly prepared starsan solution, not just water. That way if your airlock fluid gets sucked into the fermenter, it won't infect your beer.

 

Quick question on FG. How do I know what the FG is supposed to be? I agree with and have done the 2 hydrometer readings a few days apart after 2-3 weeks in the primary and when they are the same I know that the yeast is done working. However, how do I know if it fermented as much as it should have, is their a calculation/calculator available. OG divided by x = FG. I guess the follow up to that question; what can be done if the FG is not reached? re-pitch more yeast, wait it out etc? Thanks!

 

Lots of good advice in this thread. I agree with those who say there really is no need to rack to secondary. If it were my beer, I would just let it sit for another ten days or so. Yeast perform many important 'clean up' functions after primary fermentation is over, and it'll do that most quickly and effectively if you just leave it on the cake.

One really important point: There is almost never anything to be gained by trying to rush things, and almost never anything to be lost by giving the beer a few extra days or weeks to finish off and condition. Patience, grasshopper.