Relaxing in the order you specified -
Initially the d values are <t = 0, u = inf, x = inf, y = inf, z = inf>
(x, t) <0, inf, inf, inf, inf>
(y, z) <0, inf, inf, inf, inf>
(u, t) <0, inf, inf, inf, inf>
(y, x) <0, inf, inf, inf, inf>
(u, y) <0, inf, inf, inf, inf> <--Upto this no update because no relaxation started from non-inf
(t, x) <0, inf, 7, inf, inf>
(t, y) <0, inf, 7, 12, inf>
(t, z) <0, inf, 7, 12, -3>
(z, x) <0, inf, 4, 12, -3>
(z, u) <0, 12, 4, 12, -3>
Second iteration
(x, t) <0, 12, 4, 12, -3>
(y, z) <0, 12, 4, 12, -3>
(u, t) <0, 12, 4, 12, -3>
(y, x) <0, 12, 4, 12, -3>
(u, y) <0, 12, 4, 12, -3>
(t, x) <0, 12, 4, 12, -3>
(t, y) <0, 12, 4, 12, -3>
(t, z) <0, 12, 4, 12, -3>
(z, x) <0, 12, 4, 12, -3>
(z, u) <0, 12, 4, 12, -3>
Since it didn't change after second iteration, this is the final answer, which matched yours. Also there is no negative weight cycle, because of no change in entire iteration.
Note - Had the order of edges, been different, we might have expected change in second iteration.