Voltage still present after breaker is off
Before I started, first thing I did was turning off the breaker to the car charger, then I used a non-contact voltage tester, which buzzed on both red and black wires, but not white or ground. I did some research and people were saying that those voltage testers are not very reliable and can pick up phantom voltages. So I bought a multimeter, and it showed 120-125V when I measured between red/black and ground.

Yeah, that's energized, alright.

Before I started, first thing I did was turning off the breaker to the car charger

That's where it went wrong. The panel labeling is wrong.  (or remote possibility, the wiring).

There is no main breaker in the breaker box, there is a power shut off breaker outside my unit but it is locked by the utility company.

That's not legal, they can't do that!  It is literally a Code violation to deny you access to your own main breaker, unless you are in a hotel or dormitory where supervisory staff is on-call 24x7 to reset it.  And they know that and the power company has no &quot;skin in the game&quot; anyway, they have no interest in doing that to you.
I suspect you actually have a meter-main, which provides an outside main disconnect for the fire department's convenience.  This will become Code when California adopts NEC 2020, but meantime, many municipalities already require it.  This contains both the meter and the main breaker.  It must by law have 2 separate compartments :

The meter compartment has a cover on which the power company can apply a seal.
The main-breaker compartment has a deadfront cover that bolts down, and  keeps curious fingers out of the busways and terminations.
Since it's outdoors, there must be a weather cover covering at least the main-breaker area.  This can be locked by the homeowner to stop pranksters.  (the fire department has a master key).

So maybe you misunderstand how the doors work, and saw the PoCo seal on one part of it and thought it controls the whole thing.  Perhaps the weather door is sticky or weird-to-open in some way. (some you lift the whole door straight up before it can swing, this is done to create a weather seal).
Otherwise maybe the weather door goes over the meter too, and the PoCo sealed it by mistake.  Get em out there to fix it.