Most providers would not have prescribed doxycycline (or anything else) in this circumstance, unless the person's partner was known to have an STD. Doxycycline covers some STDs, but not others; good for chlamydia, poor for gonorrhea, for example; and of course no activity against viral problems like herpes, HPV, or HIV.
Therefore, how long to wait to be sure you are safe for other partners has little do do with doxycycline, except for chlamydia. For that infection, you're probably good to go after 4-5 das. For all others, you need to wait 2-3 weeks and make sure you don't develop symptoms that suggest infection.
Having said that, the risks probably are low in general. But there is no way to give 100% assurance.
Good luck-- HHH, MD
When you say for all others what do you mean?
All other STDs except chlamydia.