Your advisor is incorrect, as what you are doing is the lion's share of improving credit- low utilization, on-time payments, and good account age. Your utilization is 0 (which is great), and your AAoA (Average Age of Accounts) is constantly increasing. Your payments are being reported as on-time. Generally speaking any use of the cards will result in a statement being issued (even if the balance is 0). The statement being issued results in the reporting agencies being updated and the the accounts being "current."
Some people believe that showing some balance periodically will "help," but all data about this is anecdotal, and the FICO scoring models are not public. There's never been any official confirmation that showing a balance on a statement has any positive effect, whereas it's known that showing utilization over certain percentages has a negative effect. If you're at all concerned that one of the many versions of the FICO algorithm (there are about 3 dozen) will hold this against you, you can wait until the statement date to pay off your cards, which will mean the balance as of the statement date will be reported to the agencies. However, if your credit limits are low and this results in your utilization jumping above 10%, you will see a little hit. If it goes over 30%, you will see a larger hit until you have a month where the utilization is reported as decreasing. If it's higher still, you'll see an even bigger hit.
This is one of the big reasons that credit card churning has a net positive effect on credit scores-- your overall consumer credit available goes way up, and generally this has a favorable impact on ratio of utilization.