It has always seemed to me that within the English language until implies that something will continue occurring before a certain point, but will cease thereafter.

"My dog will stay inside until I get home" implies that after I get home my dog will not be inside.

Is that implication built into the language, or is that a false assumption that I've always had?

Thanks!

Your assumption is correct in your example. If it were not, there would be little point in saying it in the first place.