Two arguments for addition taking precedence over (being done before) the max or min:

In a max-plus algebra the addition plays the role of multiplication, and is denoted as such, while the $\max$ plays the role of addition and is denoted as such thus since multiplication takes precendce over addition this translates to addition taking precedence over $\max$; see Max-plus algebra

In various programming languages (C and related, in particular) arithmetic operations happen before comparison, and logical operations, and assignment. (I did not see really an exactly matching operator but if it is analogous to anything than I'd say something of the three I mentioned, and the all come latter.) See C operator precedence for reference.

That being said, I do not think there is a clear and universal standard, and what is reasonable for you might depend on your context. In any case, I think it will be desirable to state what convention you use, and rather to use some paranthesis if there is risk of confusion.