They pay for your night stay for interview at the hotel. And yes, they don't pay for your travel to the interview. Also true they don't pay for "your initial" flight to training. They do however give you $100 in your first paycheck as some reimbursement for that flight to initial training.
All of the tickets they buy are full fare revenue seat tickets. They used to buy tickets to training and people wouldn't show up. Obviously that was an expense that they didn't want to keep paying if someone changed their mind. Their philosophy is, if you get yourself to training, we will gladly take care of EVERYTHING else from there. And they do. I'm extremely happy with my decision to come to Omni. I spent 10 years at the regionals and I love flying the long haul stuff.
The dynamic operation that they run will probably be some of the best experience you will do in your career. There are no "canned" destinations at this company. And the training is tough, because it's old school, but fair and you will come out knowing that you can accomplish any kind of training out there.