Is it documented in the FFIEC exam manual or anywhere else what types of transactions are exempt for Phase II exemptions? Are any other types of transactions besides deposits and withdrawals that are run through the account exempt?

If you mean cash exchanges or monetary instrument purchases - if they do not run through the account they are not exempt.

The key words are in 103.22(d)(2)(vi): "To the extent of its domestic operations and only with respect to transactions conducted through its exemptible accounts, ..."