Is there a bias in top tier PhD admissions at top tier universities to favor those with undergraduate degrees from other top tier universities?

Excuse my short answer: absolutely.

Obviously, a school with a good, or even a great name, will give a candidate a big boost in his/her application. This is a rational decision: the recruiting committee wants to minimize any risks and they don't have much time to delve seriously into the history of each candidate. So if you graduated from a top school with excellent credentials you will have an edge over those with equal credentials but lesser perceived schools.

Good references from colleagues of faculty in the department you're applying to, and good ties with your school are also strong factors for admission.

Congrats on getting accepted!

There are a lot of variables here, so it isn't just where you went to undergrad, but that is definitely something admissions look at. Why wouldn't they? There is likely a correlation with going to a great undergrad, doing well, and then being successful in grad school.

Top schools get the top applicants from around the world. I can't imagine how difficult it is to compare such great applicants in any meaningful way. All else being equal, where the student went for undergrad could very well be the deciding factor. It is also a measurement that certainly anyone reviewing applicants knows a fair amount about.

There is also a lot of info we don't know about you (e.g., what you wrote in your letter, what your letters of rec said, etc.)

Again, congrats on getting admitted!