The dual degree program you are looking at offers you a bachelor's degree in physics from NGSCU and a bachelor's degree in engineering from Ga Tech, Clemson or Mercer.
You would earn two Bachelor of Science degrees. Normally these are 3+2 or 2+2 programs where you would attend one school for 2 or 3 years and finish at another school for the last two years.
I am not sure one can double major in engineering and physics in 4 years. It would be tough, IMO.