That sounds correct. All three invoices are not yet at their due dates. So they are considered current. When the February invoice goes past its due date, it will shift to the 1-30 column. In March, the second will shift to that column and the February invoice will shift to the 31-60 column. And so on.
Accounting systems record what has happened. They do no predict the future. The potential for future cash inflow is represented on your balance sheet in your Accounts receivable balance, assuming you are using accrual basis accounting. If you are using cash basis accounting, there is no such information. That is one reason accountants prefer accrual accounting.