I prefer to think of our as the equivalent of no strict 'vars' for a single variable, but in reality, our creates a lexically-scoped variable aliased to a package variable.
is the same as
alias my $var = $__PACKAGE__::var;
(Syntax issues aside.)
Unlike blocks and files, packages aren't lexical scopes. Switching package neither destroys the our variable (because the our variable is lexically scoped) nor change to which package variable the our variable is aliased (because package doesn't know anything about the our variable).