Also, without getting too far down the rabbit hole of an EE degree, understanding the difference between a current regulating supply and a voltage regulating supply.
Current = amount of flow
Voltage = pressure
So again, if you use a current regulating supply like the JWA unit, you set the current and it senses the current through the circuit and changes the voltage output to limit the current through whatever the load is. This is why again, when you had the single LED begin conducting, the voltage the regulator output lowered to limit the current through that LED that was conducting,. Your LED strip, being a strip might have series wired LEDs and thus require a higher voltage, not to mention it also probably has current limiting resistors. So again, with a current limiting power regulator, it varies the output voltage output so that the resulting resistance of the load maintains a limited current.
Conversely, since we are putting LED strips that already have a current limiting resistor, and then we add single LEDs in parallel and properly add each one with a current limiting resistor- now ideally we use a fixed voltage output regulator. That's because again we took the step to add the resistor for each LED and so we work from an assumed source voltage to achieve a certain limited current.
I personally tend to use a fixed voltage regulator for LED circuits and then use an appropriate current limiting resistor for each LED. But more typically, I'm just using a strip that already was designed for fixed voltage.
You can use a current regulating supply regulator and in some ways, there is some safety in that it will limit to a very small current in the event you make a mistake or miswire something. That said, again, where you go hooking up multiple LEDs or strips in parallel, there is a chance when using a current limiting configured regulator, one LED strip conducts first and "steals" the current from the others in parallel.
The fact is, either mode of regulation limits in some way the circuit. That's why you can use a current regulator and as long as the load is fixed, you set the current and it results in a voltage and current through the circuit. However, a fixed voltage regulator only sets the voltage. The current is based on the resistance of the load. That is why you must then use individual resistors on LEDs to limit the current through that device.
The LM317 regulator can be used in either mode- current or voltage regulation. It's all about how a board is designed and configured.