At Empowered Academics, PSP stands for our Personalized Support Program.  It is how we help support homeschooling families through an independent study approach. 
In the homeschooling world, PSP can also stand for Private Satellite Program.  Enrolling in a PSP is one of the legal ways to homeschool your child in California. Once a student is enrolled in the PSP, the parent becomes their child's homeschool teacher under the umbrella of that school.

No. Homeschooled students are not required to have immunizations. 

Students homeschooled do not need to be vaccinated.  Student immunization records (even if BLANK) must be kept on file by the school (public/charter, or private) your child is enrolled in (CA Dept. of Health form PM286B), regardless of the presence or absence of any vaccines. If your child does not have vaccines, you may submit the required blue card with your child's information on it and leave the vaccine portion blank (or write "SB277 Exempt- homeschool").   
Records must also include a physician's health exam report, or a waiver (required CA Dept. of Health form PM171B-waiver, and optional Oral Health-waiver).