Is there any problem in running Arduino logic to 12V LEDs?
The signalling of those LEDs is 5V and the power supply 12V. Basically you have a 5V-powered chip with constant current sinks driving LED chains that are powered from 12V. The 5V power for the chip is created from the 12V power for the LEDs. So, you need to:


Provide +12V and GND to the chain of LEDs from a 12V power supply
Connect the data line to an Arduino
Connect the GND connection to the Arduino as well.


Nothing more is needed.