Operator precedence and associativity in C#

Sure - it's simple a matter of precedence. The (Microsoft) C# specification lists operator precedence in section 7.3.1 (in the C# 4 and C# 5 specifications, anyway; it's 7.2.1 in the C# 3 spec), although that's only really an informative table - it's really governed by the grammar.

Anyway, the null-coalescing operator (??) has lower precedence than the binary addition operator (+) so your first code is equivalent to:

int? i = 1;
int j = i ?? (2 + 1);

As the value of i is non-null, the right hand operand of the null-coalescing operator isn't even evaluated - the result of i ?? (2 + 1) is just 1.

Compare that with your second example, where the null-coalescing operator expression again evaluates to 1, but then 1 is added to the result of that. It's effectively:

int tmp = i ?? 2; // tmp is now 1
int j = tmp + 1;  // j is 2

Associativity is irrelevant here, has it only controls the ordering/grouping when an operand occurs between two operators with the same precedence.