The thing you need help with is understanding:
(a) what it means for a credit card to report a monthly balance to a credit bureau,
(b) when the CC issuer does that, and
(c) what amount they will report.
Only after you understand that can you understand what AZEO is and whether it has any value to you. (AZEO is a very narrow instance of controlling (c) above.)
There are three big credit bureaus: Experian (EX), Equifax (EQ), and TransUnion. These are like three different warehouses that store information about your credit history. A given creditor (Amex, Chase, etc.) might report to only one, only two, or all three. In general your creditors will likely report to all three.
When we say that a creditor is reporting to a credit bureau, it means they are updating the bureau on all the most recent details of your account: what type it is (credit card, loan, etc.), how much you owe on it at that moment, what your credit limit is, whether you have been late in making a payment, etc.
That takes care of
(a) What does it mean for a credit card to report a monthly balance to a credit bureau?
Next is:
(b) When does a CC issuer do that?.... and
(c) What amount will they report?
The answer is once a month. Almost all issuers will do this just after the monthly statement prints, and the amount will be whatever is listed at the top of the statement. The statement balance will include your current balance at that instance plus any interest and fees.
Part of the reason you are unsure how a, b, and c work is that you are not used to regularly pulling your credit reports from the three bureaus and comparing the report (which lists all your accounts and the amounts last reported) with your credit card statements. You can fix this by joining Credit Karma ASAP. Ignore Karma's scores, but print out their reports (TU and EQ) once a week so that you can see this whole process in action. Once you get really secure in understaning how everything works, you won't need to pull your reports all the time. But for a brief while you need to do this so that you can understand.
Go back and review what I have said so far. The way you have described what you are currently doing, your major cards always have statements showing a positive balance. Go to Karma, compare the reports and your actual statements, and you will see that this is so.
Now we come to the idea of you controlling how much the CC issuer reports. Since the CC issuer reports whatever is on the statement, if you want that card to report $5, you need to pay down the balance to $5 shortly before the statement prints. If you want it to report $40, pay it down to $40. And if you want it to report $0, pay the balance to $0.
AZEO is a narrow technique where you control your balances so that all are reporting $0 except one (All Zero Except One) -- with the remaining card reporting a small positive balance. It is a helpful rule if you are preparing for an important credit application (car, house, etc.) since FICO models like it a bit better when it sees most but not all of your cards showing a zero balance.
No FICO models care about that long term, however, since they do not look at the history of your balances, just the most recent one.
Thus AZEO might have some value in the 40 days before a major loan application (may get you a few extra points) but it no way helps you build credit long term. To do that, you just need to use your cards, pay on time, keep your utilization fairly low (under 29%), etc. Do that and your score will increase over time.
