RGB LED Beginner

I recently purchased an RGB LED strip from Home Depot: LED Strip

It comes with it's own infrared controller and driver and works great using the driver and controller it was packed with.

Looking at the tape, it appears as though there are resistors for each set of three RGB LED's like this schematic: LED Schematic

When I remove their driver controller and apply 12V from a bread board the green and blue light up at full brightness, but the red is very dim. If I light all three at the same time the light is not white, it has a very blue / cyan tint.

Do I needed to use PWM to mix the colors properly?

Should applying 12V to the red channel put them at full brightness?

I read somewhere that you can use PWM to drive LED's at a higher current than they are rated for. Could this be what the controller that comes with the strip is doing?

Is there a way to verify I have the correct schematic using a multi-meter?

Thank you for your help.

I read somewhere that you can use PWM to drive LED's at a higher current than they are rated for.

A common misconception, no you can't without accelerating the aging and life of the LEDs.

the green and blue light up at full brightness, but the red is very dim.

That is unusual because the Red LEDs have a lower forward voltage and so should should take more current and so be brighter for a given voltage and resistor value.

Are the resistor values the same? You can measure them with your meter.

Is there a way to verify I have the correct schematic using a multi-meter?

Yes it should be possible.