One of the reasons that why birds sings at night could be that they get disturbed by the strong winds or rainfall that has woken them up from the sleep. Another reason for the birds to sing at night is predators. If they see some danger or any animal that can harm them, their eggs or even their nest they felt disturbed and starts singing aloud to alert other birds about the danger and they might also be searching for the help to save them from the predators.
One reason for their singing could be light. During night street lights are switched on and they give enough light that the mockingbirds can mistake it as the day. So they start calling for the other birds too.
Many birds that sing during the day time also sings in night under the artificial light as they misinterpret it as the day instead of night. These birds are European blackbirds, robins etc. nightingale also sings during the nights and it sings the sweetest during the night time. In fact the birds nightingale can sing anytime in the whole day of twenty four hours.
So we can say mainly the birds that sing during night is because of the disturbance which can be because of winds, rain, predators or the light which they take as the day.