The fans that come in with the case only plug directly into a molex connetor from the PSU.
That adapter you listed won't work in your case. It's meant to power a fan with only a 3-pin plug into a molex 4-pin power connector.
If you want to power the fan from the motherboard, get different fans. Most come with a 3-pin connector that plugs into the mobo, and includes a 3-pin to 4-pin adapter to plug into molex from PSU.