At present the new railway station is about half a mile from the current terminal building, and shuttle buses will be needed to transport passengers from the current terminal. However there has been a slight delay to the opening of the new station, so the shuttle buses will initially go to Rochford station which is only 1 1/2 miles away.
The new station should be open very shortly (certainly before the summer), which is directly in front of the new terminal which is still on target to open on October 1st.
I admit the current situation is less than perfect, but the whole experience should be no worse than at Luton, with the far shorter processing times at Southend. At least the shuttle buses are free, unlike Luton.