Trying to make sense of this always block

The behavior you mentioned is what I would expect... I think I never write combinational code in always statements like that. To me this would be much easier to understand ....

assign t1_next = (n == 0)? 0 : (t0_reg + t1_reg);

assign t0_next = (n == 0)? t0_reg : t1_reg;

assign n_next = (n == 0)? n : n - 1;

If you are not familar with the terinary operator this is what it means:

assign signal = (conditional)? true statement : false statement;

So above when n equals 0 the statement before the colon is used, otherwise the statement after the colon is used (2:1 mux). If you use something with more statements then I recommend using case statements instead to implement the mux since a casescade of terinary operators uses priority (unless that's what you want).