I've found the answer to my question in "Molecular Systematics" 2nd ed.
"A disadvantage to the complete rejection of information on transitions [*referring to transversion parsimony] is that, while transitions may become saturated over long evolutionary distances, they may nonetheless be highly informative with respect to relationships among closely related taxa. One way around the dilemma is to assign greater weight to transversions than transitions, without going so far as to give transitions zero weight, as does transversion parsimony."
"Because of the biochemical properties of the various amino acids, there is often little selection against changes between amino acids having similar properties (e.g., between aspartic and glutamic acids). If changes between similar residues occur very frequently, perhaps we should ignore them as well (or at least give them less weight). The generalized parsimony method can be used to implement this strategy...with the weights derived from the matrices presented by Dayhoff...or Henikoff and Henikoff."
This is OPPOSITE to what would be done in an alignment process where, for instance, conservative amino acid substitutions would be favoured.
You're correct, the probability transition matrix will remain the same in either use (alignments/inference) but the way the values are used are in opposite directions; high values are used as up-weights in alignment but as down-weights in inference.