No. Equiniti will never have access to your linked account without your instruction. You have complete control over your accounts. Transfers will only take place if and when you request them. Please note that the DDI will expire if you do not transfer money into your account for a period of 13 months.
All Direct Debit instructions are covered by the Direct Debit guarantee which means that if a mistake is made, you are entitled to an immediate and full refund from Equiniti Savings.