The adapter in the photo in your link is designed INcorrectly if that photo is accurate. Look closely at the ones you have. The photo shows that, on the large Molex connector, the black wire is in the END hole and the red wire next to it. That is REVERSED! The connections at the other end on the small male fan connector are correct.
If that really is what you have, you may be able to fix them. There are two ways (do only one):
1. Cut the wires a little away from the connector and then re-solder them back together with reversed colors. In fact, if you do this, you can test part way. Once you've twisted the wires together the new way and before soldering, use the adapter with one fan and verify that it works.
2. If you examine the connector closely you will see that, for each pin in the plastic body, the pin has a small "barb" of metal sticking out from one side so that, once the pin is pushed into the plastic body from the back, it can't be pulled back out. With a small probe or screwdriver you can bend that barb so that the entire pin can be pulled out of the back. Do this for both pins on one connector and then just plug them back into the correct holes. NOTE that the Red wire MUST go into the SAME hole as the old Black wire, and NOT on the other end of the connector.
When you're done with either of these and plug the adapter into a PSU Molex output, the Red wire of the adapter should be connecting to a YELLOW wire on the PSU output connector, and Black to Black.
Of course, if you don't want to fiddle with this, you can return the defective products and get replacement ones that are built properly.
When connecting a fan directly to a PSU 4-pin Molex output, only those two wires are needed. No third wire is useful on such an adapter.
I do NOT recommend what Lutfij has suggested exactly. Those three devices he / she suggested are PWM hubs, not just splitters, and that is the right direction for putting all your fans under automatic control by your mobo. (The only significant difference among them is that the EK Cable unit draws power from a CPU Molex power output, and the other two draw from SATA power output connectors.) BUT the problem is that such units ONLY give you control IF both the mobo SYS_FAN header AND the fans you connect are all of the 4-pin design. Your post suggests that you have 3-pin fans. 3-pin fans plugged into any normal 4-pin system can only run at full speed, and that's the same as you would get using the adapters you have (once their defect is fixed).
There is ONE PWM fan Hub on the market I know of that can control both 3- and 4-pin fans, but still requires a proper 4-pin fan header operating in PWM Mode to do it. If you want to achieve control in this way, post back with exactly what fans you have (all of them, new ones and old already installed) and the exact mobo you have. With that info we may be able to tell if this can be done, and give you details of the particular Hub and how to use it.