This is more likely to be your supplemental tax bill.
Your effective property tax bill actually consists of three separate levy categories:
1) General Tax Levy
2) Voter Approved Indebtedness
3) Direct/Special Assessments
This blog post covers the details and how you can research what makes up a tax bill for most any property:
"Estimating Property Taxes in CA"
You were given an ADVISORY anbout a SUPPLIMENTAL tax bill, which would be sent to you in 6-9 months. (You can look through your Loan papers for it).
In the next tax billing, your Property Tax would be re-figured for your new purchase price.
The previous Tax bill was based on the last ASSESSMENT and SELLING PRICE; and, obviously, was quite different than your present Assessment.
It sounds like your taxes went up $114 per month.
When Home Prices were dropping, new buyers were getting lower tax bills, and the Counties were getting less revenue.
Now, prices are increasing, and new Buyers will be getting shocked.
California is locked in to 1.25%, (irrespective of any Mello Roos or local add-ons.) due to Prop. 13.
It is possible too, that your previos owner were benefiting from Prop 13, in that they were paying less than they would have, less than their neighbors: This would have increased the difference you are seeing.
You might go down to your local Tax Assessors office and discuss it with them; but this is my input.
Good luck and may God bless
When establishing your loan , the lender most likely also figured this into your total payment.