Answer
Barn strike occurred first.
Work Step by Step
Jose sees the strike when the light travels from the tree toward him and then from the barn toward him.
So, the time it takes the light to reach him from the tree is given by
$$t_1=\dfrac{x_1}{c}=\dfrac{300}{3\times 10^8}=\bf 1.0\;\rm \mu s$$
and the time it takes the light to reach him from the barn is given by
$$t_2=\dfrac{x_2}{c}=\dfrac{900}{3\times 10^8}=\bf 3.0\;\rm \mu s$$
Now the difference between the two times is
$$\Delta t=t_2-t_1=3-1=\bf 2.0\;\rm \mu s$$
So if the two strikes happened simultaneously, he must see the tree strike first and after $ 2\;\rm \mu s$ the barn strike.
But since he saw the barn strike after only $1\;\rm \mu s$, the barn strike happened first before the tree strike by $1\;\rm \mu s$.
