(Starting to suspect I know the identity of Persephone.)

It's ugly alright. I think it jars because it seems to be operating as an adverb rather than a conjunction, as Persephone points out, making it seem like there's a word missing. 'Immediately after' is comforting but it's a complete contradiction in terms.

My guess is this came into legitimacy by common usage so I'd therefore be wary of trying to find a grammatical rule to explain it... it's a grammatical abomination! :)

At and to are not adverbs but prepositions.

It's a noun that looks like an adverb because you've dropped out 'now at' or 'here now at' from the sentence.