Analysis:

When the method JOIN::choose_subquery_plan() decided to apply
the IN-TO-EXISTS strategy, it set the unit and select_lex
uncacheable flag to UNCACHEABLE_DEPENDENT_INJECTED unconditionally.
As result, even if IN-TO-EXISTS injected non-correlated predicates,
the subquery was still treated as correlated.

Solution:
Set the subquery as correlated only if the injected predicate(s) depend
on the outer query.