Why does my volume jump up 20dB each time a new YouTube tab is opened?

Try a restart.

Do a backup, using either Time Machine or a cloning program, to ensure files/data can be recovered. Two backups are better than one.

Try setting up another admin user account to see if the same problem continues. If Back-to-My Mac is selected in System Preferences, the Guest account will not work. The intent is to see if it is specific to one account or a system wide problem. This account can be deleted later.

Isolating an issue by using another user account

If the problem is still there, try booting into the Safe Mode using your normal account. Disconnect all peripherals except those needed for the test. Shut down the computer and then power it back up after waiting 10 seconds. Immediately after hearing the startup chime, hold down the shift key and continue to hold it until the gray Apple icon and a progress bar appear. The boot up is significantly slower than normal. This will reset some caches, forces a directory check, and disables all startup and login items, among other things. When you reboot normally, the initial reboot may be slower than normal. If the system operates normally, there may be 3rd party applications which are causing a problem. Try deleting/disabling the third party applications after a restart by using the application un-installer. For each disable/delete, you will need to restart if you don't do them all at once.

Safe Mode - About

Safe Mode - Yosemite

You are welcome. Two things you can try.

Restart the computer holding down the command - option/alt - P - R keys before the gray screen appears. Continue to hold until you hear the startup chime for the second time.

Reset NVRAM/PRAM

Try a SMC reset. The article covers when this is required, but doing this will not affect anything.

Reset SMC

A third party application is any application not produced by Apple. VLC is one example.

You are welcome.