I can't figure out what the antecedent of "this" is. But like I said, the fact that quantum jumps are not instantaneous is not and has never been controversial AFAIK.
UPDATE: It turns out that in the VERY early days of QM, some researchers (notably Niels Bohr) thought that quantum jumps were instantaneous. But it has been known and universally accepted that they are not for decades now.
