“All campuses recommend that you complete math and English as early as possible (some highly recommend completing them by the end of the fall term, one year prior to enrolling at UC)”
Basically, both sources tell me that UCs do in fact reject students that didn’t complete their English/Math requirement by Fall?
Is this true?
I can’t comment on whether it is true or not. I will say that the point is to be able to write and have a strong analytic and math background that you can then use to take higher level classes. So you need to take those courses early so your skills improve to make the most of the next level of classes.
It helps to have it done, but you’re not going to get rejected solely because of it.
I got into an insanely competitive program while a required calc course was still in progress during spring, as did another guy I know.
It’s really not something worth worrying about.
I wouldn’t stress about it. I got into all the UCs I applied to while having my transferrable math class in the spring.
I not only completed an English course in the spring, but I also broke sequence and took the advance course before the first course. I was accepted to all of the top UCs from a CSU.
If you received a C in the first course and have yet to take a second, then obviously not having them both complete early would not be advisable. However, unless they have reason to believe that you would struggle with such a course, then it will not make a difference.
Okay, so I am okay to finish English on next Spring?
Thank you very much 
You can take the last English in spring, unless it’s for TAG. I think all TAGs require the courses to be completed by fall, although I’m not sure.
Okay!
I am not aware of any information about TAG. But I’ll keep that in mind.