The Arduino Uno barrel jack input connects to a linear 5 volt regulator. These types of regulators require a several volt difference between the input and output. So you need to supply 5 volts + several more volts or at least 7 volts at the barrel jack.
From the Arduino Uno web page:
The board can operate on an external supply from 6 to 20 volts. If supplied with less than 7V, however, the 5V pin may supply less than five volts and the board may become unstable. If using more than 12V, the voltage regulator may overheat and damage the board. The recommended range is 7 to 12 volts.
With regards to a power supply. The limiting factor is current. Check the maximum current value of the power supply you are using. Compare that with the expected current of the total length of programmable RGB LEDs your are using. Assume the worst case where they are all on at full power (bright white). If the LEDs demands more current than the power supply is rated for, the voltage will likely drop and cause unexpected behavior.