Mine was modded when I got it, but I'm going to guess it was set up like a stock X2, where there was a water dump from the head pipe to the pump area. If so, you would now be making that into another water supply. Originally, it flow from the engine and be to cool the stock "head pipe", then go out the back without it ALL going down the pipe, only some would go down the pipe. Now the wet pipe head pipe has injection screws so you can tune the pipe. So now you need to supply the head pipe with water.
There are more than one way to skin this cat.
If you ride in warm water, you might run both tubes from your pump to your exhaust manifold. That way you have twice the water flowing through your engine and a back up built in, in case you plug one, then you'd feed the head pipe from your head fitting. Down side to this is that you can over cool your engine in cold water, and if you never ride in really warm water, it's overkill.
So, many will run one to the engine exhaust manifold, out the head, then to a pisser, that's all you NEED for the engine. You can add a second out from your head if you want on that extra casting "boss" and go to an other pisser. This makes sure you have even cooling water flow for both cylinders, but is not necessary.
The second "new" line (that used to be your excess water out line) will supply your head pipe with water. Some like to put it in the bottom so that the air bleeds out the top and you get consistent heating/cooling, some like to put it in the top so sand and sediment will work with gravity and flow down the pipe and out the bottom fitting. It's up to you. I have run them both ways, and both work. I currently run my second water in to the bottom and out the top. Then to a T where one goes to a pisser, and one goes to the stinger fitting. The stock Factory Pipe chamber runs a carburator jet to control water flow into the stinger, that's fine. Art at Blackjack recommends drilling out this jet to a larger size (can't remember what) and running a flow control valve that does not allow water to flow at lower RPMs to reduce water to your water box and allow for faster reving in low RPM situations. You can run without it, just like I described for now, maybe think of adding that flow control valve later.
There are two fittings on the head pipe, one needs to be in, and one needs to be out. This allows flow through cooling of the head pipe and a route for excess air to escape, or sand or whatever.
These systems flow through the engine from exhaust up and out the head. The fitting that has that rubber cap on it in that one picture is a flush fitting to back flush the engine. I don't have my current hose connection hooked up. That one by the handle pole mount. If you want to run that, having that "T" to one of your head fittings is fine. Just watch to make sure when flushing that you are getting water flushing out your pump and pissers.
The great thing about running cooling like I've described is that the engine is completely separate from the exhaust, so you can actually flush the engine with it not running. No water can get inside the engine. You only need to run the engine to flush the head pipe to keep the water from getting back into your engine. I commonly run the engine and just go back and forth between cooling systems to make sure it is all flushed out without letting the engine overheat.
If you waited till spring to figure this out, you could easily go out and overheat something