timer: don't use persietent file timestamps from the future (#6823)

Also, use the mtime rather than the atime of the timestamp file. While
the atime is not completely wrong, the mtime appears more appropriate
as that's what we actually explicitly change, and is not effected by
mere reading.

Fixes: #6821
(cherry picked from commit 77542a79)
(cherry picked from commit eb877dac)