Why the stable supply voltage present a ripple after connecting it to the testing board?
It can depend from a lot of factors, to give an example, there might be something in the testing board that ruins the ground i.e. clocks, DC/DC converters etc.

How do you measure the 1.8 V? 
How do you "see" that it is shaking? 
How much is the "shaking" compared to the clean signal?

If you want more information, you have to provide a schematic or at least some details regarding the testing board.