Although early recording techniques were primitive compared with modern studio trickery, by the time Sinatra Martin and Cole were ready to commit their work to posterity, multi-tracking was in use.
It''s likely that the singers would sing with the orchestra, although they would be 'tracked' seperately, in order to mix different versions of the vocal into a finished version. The orchestra would be miked using 'ambient' microphones so that each section could be mixed seperately, giving control over volumes and pitch levels.
Modern studios record digitally, using micrtrochip technology which has done away with the need to record onto tape, and mixing can be done directly from source material, which does give a wider range of technical input, although purists would say this is at the expense of the 'warmth' of the old 'whole-studio' sound of yester-year.