The Holy Ghost fell upon Joseph and Oliver and stayed with them after being baptized only:
"Immediately on our coming up out of the water after we had been baptized, we experienced great and glorious blessings from our Heavenly Father. No sooner had I baptized Oliver Cowdery, than the Holy Ghost fell upon him, and he stood up and prophesied many things which should shortly come to pass. And again, so soon as I had been baptized by him, I also had the spirit of prophecy, when, standing up, I prophesied concerning the rise of this Church, and many other things connected with the Church, and this generation of the children of men. We were filled with the Holy Ghost, and rejoiced in the God of our salvation.
"Our minds being now enlightened, we began to have the scriptures laid open to our understandings, and the true meaning and intention of their more mysterious passages revealed unto us in a manner which we never could attain to previously, nor ever before had thought of." (JSH 1:73-74)