anode is connected to an external +12v power supply, and that the cathodes are connected individually to pins 9-11
Huh?
The schematic on that site shows the anode connected to Vdd (that's +5V) and it shows a 220 Ohm resistor connected (in series) between each cathode and its Arduino pin. Taking voltage drop across the LEDs into consideration, the current sunk by each Arduino pin is less than 20 mA.
I don't see +12V mentioned anywhere. Am I missing something? Or what?
Is it safe to have the negative side of a 12v LED connected directly to pins 9-11 for pwm?
If you have some kind of LED module or array that is rated at 12V, there will be a specification that tells you the maximum current at that voltage. It is not safe to connect such a device directly to the pin of an ATmega unless that current is less than the CPU specification. If it's a "regular" LED and not a module or array, it won't be specified at +12 Volts. It will be specified for some maximum current at a much lower voltage (maybe 1.2 or 1.8 or some such thing).
Here's why I say that it's not safe, even though the PWM may result in an average current that is within the CPU specification limits:
What if the program crashes (or hiccups) with one of the pins low. Then the maximum current will be flowing into the ATmega pin. That's not safe unless that is less than the CPU device specification.
Regards,
Dave