Adverbial form of "timely"

The following sentence seems incorrect to me, because the adjective timely is being used as an adverb:

Payments not received timely will be returned and additional interest will be due.

That said, does timely even have an adverbial form? Timelyly?

On time is surely the adverbial phrase that would be used in most cases. John Lawler would doubtless say that striving for a single related adverb (central though this usage would be in this case) is not a wise use of time.

You could use "timeously". The word is often used in formal documents in Scotland, but is obscure in the rest of the Anglosphere.

You can use timely as an adverb to mean "in time", though this is not so common.

I'd suggest:

Payments not received punctually will be returned...