Keep in mind that the auction process is just part of the legal requirements for the lender's collection activity of last resort - and that the auction process is somewhat designed so that the lender can "solve" some of the issues by following proper procedures (for example, IRS liens can be left with just a redemption period if proper notice is given to the USA that a foreclosure will happen and extinguish the IRS lien).

Correct me if I'm wrong, but is this the overall procedure?

I am assuming the mortgage company will still pay the tax bill and I just received this bill as standard procedure from the county simply making me aware of the bill?

@Mike KelleyI am planning on taking the same steps if the home has trouble selling in 60-90 days and it is possible I will make more money if I used this procedure initially.

However, CA Civil Code of Procedure 2943 does state that the lender must provide a successor in interest (you) with a beneficiary statement that gives all the relevant info such as balance/pay off, escrow amounts, insurance info, etc. and whether the loan can be assumed.  

It can't be the $250 you need but maybe your ego needs to be massaged.

What is the normal cost, in time and dollars, of eviction procedures in Californua?

What is the procedure if they refuse to leave?

In order to evict, you do need to evict even if there is no lease in place, appropriate notice must be sent to the "tenant" and procedure must be followed.  

There are 3 typical Delinquent Real Property Tax Foreclosure procedures in the U.S.