A timestep's prediction depends on future data Consider an LSTM model with 100 timesteps, each of which with input and target data. Let f(99) be the function mapping the input data of the 99th timestep and hidden state of the 98th timestep to the output data of the 99th timestep.

The mapping f(99) of another LSTM model will be different if the other LSTM model is fitted only to the data in the first 99 timesteps. It follows that future data -- that is, data from the 100th timestep -- was used to generate the 99th timestep's prediction in the first LSTM model. 

What are the implications of this for forecasting methodology?
I think you have assumed that future timesteps also are used for learning by a simple LSTM. But, that actually is Bidirectional LSTM which learns from the past as well as future timesteps. Simple Recurrent Neural Networks don't have the access to future input information. You might want to refer to a book on recurrent neural networks. You can also look this question on cross validated for training an LSTM.