We have updated the cyclical process that defines a second, but still, this definition is only valid near the earth, as the caesium atom transition process is affected by the gravitational potential well of the earth (General Relativity), plus the effects of our motion wrt the CMB (Special Relativity).

I assume these effects are really small, but if we want to define a kind of "universal second", we should remove the effects of GR and SR we experience here on earth.

This "real second" would last the 9,192,631,770 caesium atom transitions as if measured in deep space (far from any gravitational potential well), and with no motion relative to the CMB. It will be a bit smaller than the one we experience here on earth.