The game does not generate PIDs "using" a specific TID/SID. PIDs are randomly generated, and whether one is shiny depends on your TID/SID. Editing your TID/SID won't change how the game generates PIDs, but it will change which PIDs are shiny. If you copy your newly caught Pokemon over to your old save and change their TIDs/SIDs, there's a slim chance (1/4096) they could become shiny.
Every combination of TID/SID has 2^20 PIDs that can be shiny, out of a total of 2^32 possible PIDs. When a Pokemon is generated in-game, a random PID is rolled, and the chance of a shiny PID is thus 2^20 / 2^32 = 1/4096. Having the Shiny Charm rolls two additional PIDs, and the Masuda Method rolls five additional PIDs, effectively octupling the chances of obtaining a shiny PID if the methods are combined.
If a Pokemon is shiny locked and the game happens to roll a shiny PID, the PID is forcibly changed to become non-shiny; conversely, if a Pokemon must be shiny but a non-shiny PID is rolled, the PID is manipulated to become shiny.