Hi.
I think I did not understand what are you asking.
Eevee is GPU (OpenGL).
Maybe you did not find Render engine selector and what you call “Eevee” is simply open your old Cycles scene in Blender 2.8 and Render. It is still Cycles anyway (surely CPU in your case because you did not select GPU from user preferences). To select Eevee, you should do this:
You do not expect to open old Cycles scenes with Eevee and it looks good in the first instance, you must make extra configurations from Render tab, Material tab, or configuring Light Probes for example.
You can download sample scenes to study from here:
In addition to the configuration I showed in the image, in new versions of Blender 2.8, in some of those scenes it may be necessary to “Bake indirect Lighting” from Indirect Lighting item in Render tab.
And you remember, do not overwrite your old 2.79x .blend files with the same name from Blender 2.8!
Just in case, GPU selection is only for Cycles. Eevee uses the GPU configured as primary display, where you have the monitor connected. So if you can open 2.8 and select Eevee, it should already be using your GPU.
something strange
I did it on my old desktop with a very basic video card
and it took 30 seconds which is less then on the other I7 and big video card!