I entered the USCG in 1985, and we had to do urine tests regularly. I don't know exactly when that practice began, but I do remember that they were still working out the best practices for the procedure. It had not been common practice for very long, I don't think. Maybe just a couple of years. I remember the "old" guys at the time bitching about having to go through it. It was fairly new.
Even then, the drug testing was a separate program from the ordinary physical. Physicals were done for the usual medicals reasons. I don't remember a drug test even being part of it, since that required elaborate arrangements with labs to perform the testing, and it required two-person integrity on all the sampling and marking of samples, and lots of special forms to fill out to meet the specs of the process. No point in doing it for the physical when there was already an apparatus in place to deal with drug testing as a program on its own.
http://www.alwaystestclean.com/articles/atc_article_40.htm
1981 according to this article..