@Uluv_Gabehorn You are indeed correct in your assumption. As the information on Help Desk: Alpha and Omega Clone states, in regard to Multiple Clients running at once:
Alpha Clone
- Not available, if there is a client logged into an Alpha account, no additional EVE clients can be started past the character selection screen, independent of their state.
Omega Clone
- Multiple Omega accounts may be logged in at one time, as long as no Alpha account is actively logged into on the same computer.
So just to clarify it; even if you have an Omega account and an Alpha account, you can’t have them logged in at the same time. As it is stated within the limitations of Alpha Clones.