WiLL MY MOM END UP PAYING TAXES ON QUITCLAIM DEED HOUSE??

Hi, my dad ped away last May, my mom and dad was joint tenant on owned and payed off house. so lawyer QUITCLAIM DEED the house on my moms name and also AFFIDAVIT-DEATH OF JOINT TENANT with death certificate attached and it went through the county, we live in California. 2 months before my dad ped away, we made our patio to a room to the same house with county permit. ALSO THE QUIT CLAIM DEED SAYS "REVOCABLE TRUST TRANSFER EXEMPT FROM REAPPRAISAL UNDER PROPOSITION 13".....WHAT DOES THAT MEAN,,,ALSO WE RECEIVED NOTIFICATION OF ESSED VALUE, IN GENERAL INFO IT SAYS: PROP 13 PROVIDES THAT REAL PROPERTY MUST BE APPRAISED AT MARKET VALUE UPON CHANGE IN OWNERSHIP OR UPON COMPLATION OF NEW CONSTUCTION.......I FEEL LIKE WE ARE MISSING SOMETHING TO FILE. OR WE GONNA GET HUGE TAX,,,,PLZZZZZZZZ HELP I AM NOT FAMILIAR WITH THIS AT ALL....ALSO REVOCABLE LIVING TRUST WAS MADE TO MY BROTHER,,WHAT DOES THAT MEAN IN THE FUTURE FOR HIM.,WILL HE HAVE TO PAY TAXES OR NO