Man, I'm having similar problems and hope someone can help me. Found
this thread/forum via google typing stuff in....

This is a very recent development. About 10 days ago, I changed
the...the thing that stops the water in the toilet...they don't even
name it in that howstuffworks link. It's the ball thing at the end of
the chain. My last one, something rotted away, so I bought a new one.
Now, whenever the toilet is flushed, there's this massive vibration
happening immediately after the toilet is filled with water. It's
crazy! I've tried just turning off the toilet and it still vibrates.
It's vibrating right now as I type. So it's not just 5-10
seconds....
Couple things: I don't know...the filler valve is that big thing that
floats, right? You know, as soon as I replaced the plug/chain deal,
when you flush the toilet you have to hold the handle down until it's
done flushing, it didn't just float/regulate and let you walk away.
That's definitely a symptom of my main problem, right?
Should I get out of my house? Should I replace everything inside the
toilet?