I know this is an old thread, but i had the same thing and googled "toilet vibration when flushing" and this thread came to the top of the listings. So figured i would put the answer to how i fixed it for others to read.
My toilet would vibrate so hard when it was filling even the air freshener on the top would fall off and i thought it was the pipes behind the wall loose, as you could hear them banging as well.
I was about to call in a plumber, but after reading this i decided to take a look myself.
Our cistern, has a long arm with a float, the valve that turns the water on and off from the float has 2 threaded hand nuts on it which i took off, this gives access to the 2 washers, the diaphragm washer that the float arm pushed on and the seal washer that stops the water itself.
I bought this morning from plumb base one of each. The diaphragm cost 41p and the seal washer comes in a pack of 5 with the cone shape thing it fits on for £1.54 for the pack.
I noticed the bottom seal is slightly thinner on the new one, but for the price got them anyway.
I changed them both and it didn't vibrate, but the water wouldn't turn off it constantly dripped, so put the old bottom seal back in and it worked fine (stopped the water and the vibration), put the old diaphragm back in and it vibrated.
So now it has the old bottom seal in and the new diaphragm top seal and it works perfect, water turns on and off perfectly and there is no noise at all.
Thanks for all your help and advice guys its saved me about £40 for a plumber to come out and do the same job that cost me 41p
Ian