Vaccinations- Any vets around?

[Evenstar]

I have rehomed a 6 month old Pomeranian today, the owners started his first course of vaccinations but only had 1 injection. He had the second injection of a new course yesterday, the previous owners took him out to the park yesterday and say their vet told them that would be OK. Is this correct or would the normal waiting time apply before going out? He has not been socialised with other dogs or people so obviously the sooner I can get him out the better, but I don't want to take any risk. Thank you