Do you need to check out with the US immigration when you leave back home on a B2 visa when exiting through Tijuana Airport?

It is possible that her departure from the US was not accurately recorded, which could lead to some questions at US immigration when she returns. That said, this is a normal and not uncommon situation, and she certainly hasn't done anything wrong, assuming she left the US before the end of her period of admission.

What she can do is lookup her I-94 admission record online. That site will tell her what records the US Government has for her arrival and departure. If everything is order, then great: there's no problem. Even if not, it still shouldn't be an issue. Here's what that page says about discrepancies:

If you have a paper form I-94 and depart by land, you can turn the form into Canadian Border Services Agency (CBSA) upon entry into Canada or to CBP at the port of entry prior to entering Mexico. If you received an electronic I-94 upon arrival by air or sea and depart via land, your departure may not be recorded accurately. A departure will be recorded if you depart via land and re-enter the United States prior to the expiration date stamped in your passport. If you are not a resident of Canada or Mexico and you receive an electronic I-94 and depart via land, but do not re-enter the United States prior to the expiration date stamped on your passport, you may want to travel with evidence of your departure into Canada or Mexico. Evidence of departure can include, but is not limited to, entry stamps in a passport, transportation tickets, pay stubs and/or other receipts. A traveler can request an entry stamp from CBSA when entering Canada or from the Instituto Nacional de Migracion (INM) when entering Mexico.

As she is a resident of Mexico, the advice to travel with proof is not operative, but in the event that she receives questions, it wouldn't hurt to carry some documentation that she left on time when she visited last, such as a copy of her boarding pass from Tijuana.

If she still has a paper I-94 form that didn't get turned in, she should follow the instructions on this page to have the record corrected.

I was confused as to how this all works, so I googled it and came up with THE CBX SKYWALK which is the bridge directly between the USA and Tijuana airport.

On that page it says:

The skywalk is only accessible to ticketed Tijuana Airport passengers who have boarding passes for flights departing within 24 hours or having arrived within 2 hours. You'll be required to go through U.S. Customs & Border Protection if you are traveling north, and Mexican Customs & Border Protection if you are traveling south.

My guess is that they already know all about your Aunt and doing what she did is perfectly normal and done by thousands of people per day. Thus as long as she has the correct visa etc to arrive at LAX she will be fine.

Plus I don't think that the US is concerned too much about people sneaking out of the country via a public route. It's coming in that they are rather anal about.