You can crunch numbers all you want, but the greatest value Tulo has given the club is that now they believe they are good. Also I think Tulo's D is much better then Reyes so the pitchers trust that when a ball is hit in his direction it will be an out. Dramatically changing how you pitch and therefore making you more effective, therefore resulting in fewer RAs. WAR is not built to calculate all of that.
Getting back to believing. If you believe you can win, it does not matter what the score is before the game ends, you know you have a chance to win. If there is any doubt that you can win, then if near the end of the game comes and it seems out of reach, a win will rarely happen. Right now the BJs believe they can win each and every game and that started with the trade for Tulo.
For evidence of belief, look at what happened in the 1990's when the Twins started the year with 25 virtual nobodies who all believed they could win and kept that belief all season. They won the WS that year. If the BJs go on to win the WS, it does not matter that stats may say Tulo WAR ended at -4.0, the belief that got then there started with that trade and that is what makes that trade very important and valuable.