Hello. After my sprinkler backflow valve was tested this summer I began hearing vibrations in my pipes after either of my 2 toilets are flushed. It vibrates worse if I turn on the sink after flushing the toilet. After searching a bit online, I replaced the fill valves in both toilets. It's still doing it. In fact, it seems to have gotten louder. Any thoughts?

This takes you and a helper. You flush and the helper goes around the house and grabs hold of the cold water pipes. They will vibrate enough to feel where the vibraytion is happening. Frequently the toilet fill valve. Once you find which valve is vibrating then you have to service it or replace it

Do you have a PRV (pressure reducing valve)? Will be located immediately after the main shut off valve.

hkstroud - Yes, I do have a PRV.

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It vibrates worse if I turn on the sink after flushing the toilet.

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That makes me think it is probably caused by either a loose washer in the main shut off valve or defective PRV.
If PRV, it could be defective or it could have debris trapped in it. Some PRV's have screen that can be remover and cleaned.

Close main shut off valve partially to see if any thing changes.

Then start by holding the prv while the toilet is flushed, if you feel the vibration then you found your issue. If it is the prv you may be better off replacing rather than trying to repair it