Thank you for your comment. Just to clarify: in both situations you would be OK in terms of treatment.
This leads me to a second question: If the antibiotic stays in your system for a few days (therefor preventing further infection for at least a short period of time), why is it cautioned to wait a week when both partners have been treated? It feels like the antibiotic both treats and prevents in both parties, and by the time the antibiotic leaves the system (thereby stopping prevention) the infection is cured.
The usual chlam/gon antibiotics like ceftriaxone, Zithromax, doxycycline etc remain in the system for at least a couple days after the last dose. You would be protected against in this exposure. and no, you can't be treated too soon. Getting treatment even 5 minutes after exposure would prevent these STIs from catching hold.