It does not seem to be using Rasterize[Text[...], "RasterSize"] nor ImageDimensions[ImageCrop[Graphics[Text[...]]]] nor Rasterize[Text[...], "BoundingBox"] (and indeed seems to do the computation differently than png export, which leads me to suspect this might be a bug).

Consider

Rasterize[p1 = With[{nmax = 10},    Graphics[     Table[With[{v = StringJoin @@ Table["a", Mod[n, 2, 1]*10]},        Inset[Text[v],         Offset[ImageDimensions[ImageCrop[Graphics[Text[v]]]]/2 + {3,            0}, {0, n/nmax}], {0, 0}]], {n, 1, nmax}]     ]]] Rasterize[p2 = With[{nmax = 10},    Graphics[     Table[With[{v = StringJoin @@ Table["a", Mod[n, 2, 1]*10]},        Inset[Text[v],         Offset[Rasterize[Text[v], "RasterSize"]/2 + {3, 0}, {0,           n/nmax}], {0, 0}]], {n, 1, nmax}]     ]]] Rasterize[p3 = With[{nmax = 10},    Graphics[     Table[With[{v = StringJoin @@ Table["a", Mod[n, 2, 1]*10]},        Inset[Text[v],         Offset[Rasterize[Text[v], "BoundingBox"][[1 ;; 2]]/2 + {3,            0}, {0, n/nmax}], {0, 0}]], {n, 1, nmax}]     ]]] Export[FileNameJoin[{NotebookDirectory[], "foop1.pdf"}], p1] Export[FileNameJoin[{NotebookDirectory[], "foop2.pdf"}], p2] Export[FileNameJoin[{NotebookDirectory[], "foop3.pdf"}], p3] 

In Mathematica, only the first one is correctly aligned:

p2 looks like this:

And p3 is similar but not identical. However, when I export to pdf, foop1.pdf looks like this (screenshot):

and foop2.pdf and foop3.pdf look similar. What’s going on?