Need help with uno power supply

I need help understanding why my uno with trigger a 5v relay when connected via computer usb though will not trigger (relay bounces then stops) with alternate power supply. I have tried 5v 1amp (12v converter) and 12v 1.5amp.

What is causing this?

It did not do this when I had a different 5v power supply from a 12v converter (both converters are car chargers)

How do you have the relay wired? Can you post a drawing, schematic, or picture of what does and does not work for you.