All of the cats I have or have had or rescued all were rescued by me not from a shelter or the like.

I always take precautions & keep them seperated in a quarantine room until they are checked by a vet and have the leuk/fiv tests done. If I happen to get them to the vets right -away (within the first day or ) I still keep them seperated for days just in case they have a URI or another contagious illness that isn't showing symptoms yet.
And I always have my cats checked for luek/fiv yearly, in case it wasn't showing up yet on the first test and also to make sure they haven't caught it. They are vaccinated for Leuk but not FIV.