MAYBE - info required is not published. But to help understand, more details.
In a complete HUB the unit most likely has only passive connecting wires (as traces on a printed circuit board) and no active chips. (The Phanteks hub board in your case is MORE complicated with active chips for conversion and control.) Most hubs are really suited only for use with 4-pin fans and PWM Mode control signals. (This Phanteks Hub is an exception.) Those original PWM Mode signals sent by a mobo fan header consists of:
Pin #1 - Black - Ground
Pin #2 - Yellow (sometimes Red) - +12 VDC constant
Pin #3 - Green (sometimes Yellow) - Speed pulse signal
Pin #4 - Blue - PWM signal
The speed signal generated in the fan motor and sent to the header on Pin #3 is a series of 5 VDC pulses, 2 per revolution. The header counts these to calculate fan speed. It does NOT control fan speed, and its value is not used by the mobo to control speed, but is used to monitor for fan failure. The PWM signal (pin #4) IS the control signal used by a chip in the motor to adjust its speed.
In a Hub, the main power supply (fixed +12 VDC, Pin #2) is NOT connected to the mobo header so it draws NO current from that source. Instead it is connected to a supply from the PSU as the main power source. The Ground (Pin #1) line also is connected to the PSU. The speed signal from ONE output port (usually Port #1) of the Hub is fed back to the mobo host header on Pin #3. The PWM signal from the host header is shared out to ALL Hub outputs on Pin #4 of each port, but the current drawn from that source is minimal and NOT subject to a max current limit.
The main consideration of power limits here is the power for the motor, involving the +12 VDC line and the Ground line. There is a limit imposed by the size of the conductor wires or traces in the Hub itself, but you almost never see that spec published. Some of us assume 1.0 A and the limit is likely higher than that, but not known. But what IS known is the limit imposed by the contacts in the connector to the outside power SOURCE. This is the limit for the TOTAL current for the entire Hub load, and NOT a limit on each individual output port. For a connection to the PSU via a SATA power output, that limit is 4.5 A. For a connection via a 4-pin Molex connector instead, that limit may be more like 10 A, BUT that also depends on how heavy the wires are in the cable from that connector to the Hub.
So to the specifics of the components you cite. The Hub board in the case from Phanteks uses a SATA power connection so the TOTAL load of the Hub is normally 4.5 A, but Phanteks has specified the limit of their Hub board to be less, at 4.0 A, probably because of the active elecroinic components of that Hub design. No spec for per-port limit, but typical spec for the chip that outputs power to a single fan is 1.0 A max. The EKWB-EK Cable unit is another type of Hub in appearance, but it does work the same way as common Hubs. Its website does not provide any limit specs. From its photos one of its "arms" gets the PWM control signal from a mobo header and returns to the header the speed signal from one fan. It makes NO other connection to the host header. All power for the fans is obtained by a 4-pin Molex connection to the PSU, so the CONTACTS of that connector are likely to support up to 10 A max curent. It IS likely that those wires would allow 1.0 A (maybe more) on each output, BUT the WIRES from the connector to all of the output connectors are NOT specified, so we cannot be sure about that over-all limit.
Your last query is a little unclear because you ask about "greater than 1.0A from each header". The name "header" refers to the MOBO fan header. When you use a HUB such as these devices the current limit of the mobo HEADER is not a problem because no current is drawn from it. BUT if you meant to ask whether you could draw more than 1.0 A from each OUTPUT PORT of a particular HUB, then that question depends on the HUB design as above.
In your case, careful arrangement of pairs of fans to FIVE ouput ports of the Phanteks hub board will get you all ten fans connected, powered and controlled safely without needing to create a load over 1.0 A on any one output.