or maybe 13 billion years is from the frame of reference of the Cosmic Microwave Background? that would make more sense. I'm going to check again then edit this comment.
(i am not a physicist, not an authoritative source on this)
edit: so it turns out that the age of the universe is given from the frame of reference of the CMB rather than from Earth's frame of reference.:
> Measurements of the cosmic background radiation give the cooling time of the universe since the Big Bang
> Cosmic time, or cosmological time, is the time coordinate commonly used in the Big Bang models of physical cosmology.[1][2][3] Such time coordinate may be defined for a homogeneous, expanding universe so that the universe has the same density everywhere at each moment in time (the fact that this is possible means that the universe is, by definition, homogeneous). The clocks measuring cosmic time should move along the Hubble flow.
According to [1], the ratio is about 5.56E-10, so I guess this would contribute about a year to the age of the universe, so.. not that much. I guess I answered my own question.
However, this does pose an interesting question about the age of the universe in extreme gravity wells doesn't it? Or am I misunderstanding something?
[1] https://www.quora.com/How-much-time-on-earth-is-1-hour-in-sp...