Delta time has small random variations because neither the refresh rate of your display nor the timer measuring the time between the display refreshes are perfectly accurate. However this should not normally matter.
It's also actually correct that it varies, if your display refresh rate varies too. For example suppose a display had an irregular refresh rate: one frame was displayed for 50ms, then the next frame was displayed for 100ms. In this case the delta-time measurement should be 0.005 then 0.01, so that the motion of the game is lined up to the actual display refreshes. If you smooth delta-time or otherwise don't use the actual value, then it can actually add jank and inconsistency, as in this case the game might do something like advance motion by 75ms when the image is shown for either 50ms or 100ms, either undershooting or overshooting. Given the prevalence of variable refresh rate displays, this may be a more likely scenario than it seems.
I think the problem in this thread may be that you've jumped to conclusions. The object you showed wobbling is not actually moving. So why is it using delta-time? This appears to be a logic problem with your events. I don't think you should be using delta-time at all there.