Or either that or it sounds like it might could come under the general heading of assimilation, one. Usually you see examples of assimilation where the sounds are butted right up next to each other, like illegal from the prefix in slapped onto legal, or impossible from in + possible, but maybe it's still assimilation in a case like this.

FWIW, Wikipedia refers to it as Anticipatory Assimilation at a Distance.

But you don't have to take Wiki's word for it. There's also mention of anticipatory assimilation here. It also appears to be called regressive assimilation.