Doubtless he was claiming reimbursement of some expenses from Deco for years before he was sworn in as mayor, including while he was a councillor. During that time he was employed (at least ostensibly) by Deco and could purport to be incurring some expenses in his role as an employee. IIRC he has claimed not to be employed by Deco since he was sworn in as mayor, and without him being employed by it (at least ostensibly) Deco could not reimburse him for expenses and claim the reimbursements as a tax deduction.
However, that does not necessarily lead to either of the scenarios you posit. There is a third. He is able to get money from Deco, either indirectly via DFH (the owner of Deco) or directly (e.g., interest on so-called shareholder loans to Deco), or via his father's estate or the family trust that owns DFH, or on top of his salary as Mayor, just as he was able to do the same on top of his salary as a councillor, that would suffice to enable him to pay the office expenses, etc. that he does not claim from the City. That is not the same as saying that those sums are being charge to or paid by Deco. (If you own shares of, say, a bank and the bank pays you a dividend on those shares and you use that money to pay rent, you are not charging the rent expense to the bank.) He is no more prohibited from having an indirect ownership interest in Deco, or an outstanding so-called shareholder loan to Deco, and so on as the mayor than he was as a councillor.