Splitters are different devices from Hubs. Hubs always get all the power for their fans from a direct connection to a PSU output connector, and they always require a PWM signal from a mobo header to do their job. A HUB may be a box such as you have, or it may also be just a group of wire arms, or it may be a circuit board. So, a HUB has one arm that plugs into a 4-pin mobo header, several arms or ports (on a box like your Silverstone unit) to plug your fans into, and one arm that must plug into a PSU output (either 4-pin Molex or SATA). With one exception I know of, all Hubs can only work on 4-pin fan systems, because all they do is re-distribute the PWM signal from the mobo header to all their fans. So, ALL their fans must be of the 4-pin type to be able to use that signal and be controlled.
A SPLITTER has the single input arm and two or three output arms for fans. It does NOT have that third type that plugs into the PSU. A Splitter merely connects all its fans in parallel to the signals it gets from the host mobo header. Thus it is limited by the maximum capacity of the mobo header to supply power, and that is normally 1.0 amps total to all fans on the Splitter. A 4-pin SPLITTER (NOT a Hub) can work with 3-pin fans just fine - the fans merely do not connect to the PWM signal on Pin #4 that they cannot use anyway.
To control several 3-pin fans you can use a Splitter IF their total max current draw us under 1.0 amps, and IF the mobo header can be configured to use Voltage Control Mode (aka DC Mode).
Among Hubs, the one exception I mentioned above is the Phanteks PWM Hub. It does not just share the PWM signal out to its fans. Instead, it uses that signal to create its own set of six 3-pin fan ports that operate in Voltage Control Mode, so they CAN control 3-pin fans. Moreover, like other Hubs it does get all fan power from the PSU, so it is not as limited as a mobo header is. Its limit is 1 amp per port (Phanteks recommends up to 2 fans per port on all except the white #1 port). Now, the design of 4-pin fans includes a backwards compatibility feature so that, if you plug one into a header that uses Voltage Control Mode, it still IS under speed control - this method of control is not quite as good as using the "proper" PWM Mode, but it works. So the Phateks PWM Hub can power and control any mix of 3- and 4-pin fans. However, you have to fiddle a bit to get a 4-pin fan plugged into its 3-pin ports because they are spaced close together.