There is nothing wrong with having non-Irish accounts.
As a non-Irish resident you are not liable to tax in Ireland on non-Irish arising income.
As a UK resident, but non-domiciled, you are only liable to non-UK arising income that is remitted to the UK. If no offshore funds remitted to the UK, no liability arises.
If you come back to Ireland, as not-ordinarily resident for 3 years, you will only be liable to non Irish income remitted to Ireland.
You just need to make sure that you declare income correctly in due course if liable to Irish tax.