The noun tumbler can refer either to an acrobat who performs gymnastic tricks or to a tall drinking glass with straight sides. If you own a lot of glass tumblers, you probably shouldn't let a troupe of tumblers practice back flips in your kitchen.
Gymnasts are often called tumblers because they are skilled at tumbling, namely skills like round-offs, flips, aerials, and back handsprings. When an object is a tumbler, it's simply a drinking glass. Though today's drinking tumblers have flat bottoms, back in the 15th century they were rounded or pointed and couldn't be set down between drinks, or else they would topple over — or tumble.