First of all, the beginning of the first sentence itself does not make sense to me: "本条款约定的日期乙方必须于每月 1 日前". I suspect that "本条款约定的日期" is a heading, and that the first sentence begins with "乙方必须于..." If so, then "约定的日期" would be the same thing as "每月 1 日前", and "约定的日期不包含当日" would mean that the payment must be made before the first day of the month (i.e., by the last day of the preceding month) rather than on or before the first day of the month (though to me "每月 1 日前" seems to express that concept clearly enough).

Yes, I agree with you. The logic in this writing is not organized well.
Maybe it should be like this:

本条款约定的日期乙方必须于每月 1 日(不包含当日)前根据有关缴款通知书或帐单付清当月全额租金、物业管理费及其他各项费用，并以实际到帐日期为准。

In this way, it can be translated using a bracket.

It means the 1st day of each month is not included, you can just use
"the 1st day of each month (exclusive)" to express the meaning.