They don’t have tumblers as medieval locks were not pin tumbler locks, they were warded locks.
These were then superseded by lever tumbler locks
Which now compete with (in the UK at least, though low security ones are used as interior locks and high security one .range from back doors to gun cabinets, as a secure lever tumbler lock (5 or more levers) is harder to pick or force than a pin tumbler lock) the pin tumbler lock, which only really became popular in the mid 20th century.
So there are no tumblers in the lock as pin tumbler locks weren’t invented then. There was the Egyptian lock design which is similar to a pin tumbler lock but they never became popular in medieval Europe.
From wikipedia:
"In 1805, the earliest patent for a double-acting pin tumbler lock — one where lifting the pins too much or too little prevented opening — was granted to American physician Abraham O. Stansbury in England."