on leaving the cinema, (upon the act of leaving the cinema or when we were leaving), we went for a drink."(It tells "when" we / went)
"on hearing that my brother was planning to go abroad, (When learning that my brother . . . )I decided to talk with him." tells when I/decided
"lost for many years, the painting turned up at an auction."
describes the painting (that is had been "lost" (missing, stolen, hidden?)for many years before it showed up to be auctioned.