Are fans in PWM mode always supposed to go up and down in speed?

If I understand the manuals for the Corsair fans and LED controllers and the Node, it is the Corsair Link software ONLY that controls all of your case fans' speeds. That assumes that you have installed and connected the all the HD120 RGB LED fans to a Corsair RGB LED Hub, and then that is plugged into a port of the Node Pro unit, which in turn is connected to a USB2 mobo port. Such a system has the Corsair Link software take over all the speed and color controls for the six HD120 case fans, and settings for the mobo CHA_FAN headers will not affect them at all. Still, the actual temperature of the mobo as measured by a sensor is used by Corsair Link to guide its control actions.

Now, the Hydro Series H100 CPU liquid cooler system is different. If that's the exact model you have, it does NOT have any connection to a mobo USB2 header, so I think that Corsair Link software does not control it. Instead this unit's instructions say you have some control over the speed of the fans it uses (provided that you have plugged those into the posts on the H100's pump module) via a pushbutton on top of the pump. It does not indicate that there is any other control of its fans. HOWEVER, is that really the cooler you have? There also are H100i and H100i V2 models, and their fans are controlled differently and DO use Corsair Link to control the fan speeds on their radiators. For those latter two models, IF you connect the components as instructed, the mobo does not control the radiator fans directly, although the Corsair Link software that does the control uses the temperature sensor in the CPU chip to guide it.

Assuming Corsair Link is doing all your fan speed management, remember that it is based on actual measured temperature at a couple of points. The intent is that, as your workload changes and produces more or less heat generation, the fans are SUPPOSED to change their speeds to keep temperatures under control.

That's a different picture. So you have six fans in total, of which two are on the radiator for the H100 system, and the other four are for case ventilation. All of the fans are plugged into the LED Controller? I suspect you mean LED HUB, which has six 3-pin fan ports, a cable to a SATA power output from the PSU, and a port for connection to either the LED controller or the Node PRO. The LED controller is a simple box with three pushbuttons on it to control fan speed, LED colors and lighting effects. If you connect the Hub instead to a Node Pro, and the Node Pro to a USB2 header, then that system can be used by Corsair Link to control those effects, without using the manual controller box. I suspect that is what you have set up.

With a system set that way, there is NO connection from any part of the Corsair modules to any mobo fan header. Is that right? Well, one exception, and maybe that's a problem. The H100 pump unit has two cables coming from it. One goes to a female 4-pin Molex power output from the PSU to get power for it. The other normally plugs into the mobo's CPU_FAN header. But the instructions suggest that this connection serves only to send the pump unit's speed back to the mobo. It is NOT used for control of the H100 system in any way. Then the normal way to power AND control the fans on the radiator is to plug them into the H100 pump unit's fan ports. But you have NOT done that.

The manuals for the H100 do not talk about any way to control the H100 cooler system other than the button on top of the pump unit. BUT the website claims it can be connected to their "Mini Commander" module for some control. MAYBE you can connect it somehow to the LED Hub you have, giving you control of both the speeds and the LED colors in those HD120 fans you're using on the radiator. How is not set out in the H100 instructions.

It MIGHT be that what you've done is correct. That is, the "fan connector" coming from the H100 pump goes into the CPU_FAN header to report its speed without any use for control of the pump. Then the two HD120 radiator fans plug into the LED Hub and are controlled (speed and LED functions) from there using the Corsair Link software, BUT if that is the case, the Corsair Link software probably needs configuration for its several different functions. It has a least three things to do:

1. Monitor the CPU internal temperature (there's a temperature sensor built into the CPU and available to the Link software from the mobo) and control the Radiator fans according to the CPU cooling requirements.
2. Monitor the motherboard temperature (using a different temp sensor built into the mobo) and control the other four HD120 fans you are using for case ventilation.
3. Do whatever you want with LED colors and display effects.

IF that's how Corsair Link works, you need to find out how to configure it for all that. Consult Corsair's Tech Support for instructions. I suspect you need to custom-configure each fan port on the LED Hub according to which fan is connected to it.