This is good info. In this case, however, one does not have two random variables. That would be the case if you had X \sim \text{normal}(t, 1) and Y \sim \text{normal}(t^2, 1) and you were interested in Z = XY. Here one is assuming a density on X such that f_X(x) = \phi(x; t, 1)\phi(x; t^2, 1), where \phi(\cdot; \mu, \sigma) is the normal density with parameters \mu and \sigma. In @Jean_Billie’s post above f_X is a weird density. If you were to write:
target += 0.5 * normal_lpdf(x | t, 1);
target += 0.5 * normal_lpdf(x | square(t), 1);
Then X would be normally distributed with parameters \mu^\ast = \frac{t + t^2}{2} and \sigma^\ast = 1. This is called geometric pooling.