I think the starter following you will not be in HG/SS, well actually it will be to a certain extent. For all we know it could only be for certain events. But I believe it will only be until after the Slowpoke well event. Reason: It seems like a significant event to change things and that your starter is nearing evolution.
I think its a really cool feature.. but does anyone think GAMEFREAK took this idea from digimon? did any body played digimon world? in that game the digimon follows you around.. and now it also has it in HG and SS.. does any one agree?
~Sparkcaster~
Yeah, what Lily stated above is right, they got this idea from Pokémon Yellow, not Digimon.
Also, has anyone thought it might be really cool if the supporting character and Silver might have their starter follow them as well everytime we might encounter them in the game perhaps?