A secured credit card is the same as a regular credit card from a credit scoring perspective. The secured nature of the card is only known by the issuing bank.
With that known, the rest of the question becomes a credit scoring question regarding credit cards. It is always better for you, the borrower, to pay off the card in full every month. This will result in you paying the lowest amount of interest (if done faithfully you'll pay none). The bank would prefer you to pay anything less than the full amount so they can earn interest. As such, their advice to you was in this vein.
Credit scoring cares mostly about utilization and payment history when it comes to credit cards. Utilization is not historically tracked, but payment history is. Utilization measures how much of a card's credit limit you're using at any given time. It is calculated using the "statement balance" on your statement (meaning it does not distinguish between paying in full or carrying a balance).
Ensure you pay the bill on time always and pull your utilization below 10% when seeking new credit.