When the conversion was made c. 1905, Model 1898 rifles in German service were re-barrelled to the "S" cartridge. The Model 1888 (Commission Rifles) were not rebarrelled; they were simply rechambered so there would be room for the necessary neck expansion with the new round. The bore diameter was not changed and apparently gave no problems. Note, though that late Model 1888's had bore sizes at or close to the groove depth of the "S" bullet.
In a high power rifle, neck expansion is necessary to allow the bullet to be released; if the chamber neck is too tight (as it could be when a round with a .323 bullet diameter is fired in a chamber with a neck sized for a round with a .318 bullet diameter), pressure goes very high. So running an "S" reamer into the old chamber expanded the chamber neck and gave an adequate margin of safety.
FWIW, the reason for the change was that the old barrels eroded rapidly, since the groove depth was only about .0035" (.318" groove - .311" bore = .007", so the groove depth is only .0035". The change was to deepen the grooves; the bore diameter remained at .311", so .323" groove - .311" bore = .012" for a groove depth of .006", a depth that could handle erosion and corrosion without the lands washing out.
When unconverted Model 1888's were issued (as to reserves), there was no confusion with ammunition; the old ammo was issued only in en block clips which could not be used in the new rifles, and the new ammo was issued only in chargers (stripper clips) which could not be used in unconverted older rifles.
Jim