continuo

Continuo is the ablative of continuus doing adverbial work: with nothing in between, therefore immediately. Statim and protinus are the plain synonyms and appear in the same slots.

Two things to watch. It is spelled exactly like the first person singular of the verb continuo, "I join together", so the part of speech has to come from the sentence and not from the ending. And with a negative it shifts sense entirely: non continuo means "it does not follow, not necessarily", not "not straight away". Cicero uses that turn constantly in argument, and reading it as time makes a hash of the logic.