Odd. I would have thought that if the new inputs were not useful the model could simply ignore them.
Unless you have rescaled the sine and cosine inputs, they are in the range -1 to 1.
Normalising the data is often a good idea. A common method is to subtract the mean and divide by the standard deviation. That gives data that is mostly in the range -1 to 1. Apparently that helps the gradients to flow properly.

A few negative values would not overly surprise me, but it is odd that they appeared only after rescaling the inputs.
Another potential issue is the shortness of the batches. Each batch goes from midnight to midnight which probably means that backpropagation through time is cut off at midnight every night. This means that for the 1am reading the backpropagation is very limited, and for the 11pm reading the backpropagation is longer, but still not long enough to take into account any effects that last longer than 24 hours.
I would suggest using longer batches at least in the initial training.