Perhaps the ancient Greeks did conceive of a heliocentric model 

of the solar system, however they may have realized that it is 

neither more nor less true than a geocentric system. In this case

 I think it seems natural that the sun and moon appear to be going 

around the earth, because this is the point of view of the user. 

I doubt the device was designed to be used by someone 

standing on the sun, therefore a heliocentric representation 

would seem very odd and rather meaningless.