Instead of looking at it with a "is this fair now" view, why not consider discussing with the employer of a promotion plan within X period. You could be honest to let them know that you appreciate the offer and you'd like to propose an alternative plan for them to develop yourself to be a much better employee in their company. This is when you could share with them that you're loooking to be X salary within X period and you understand this is based on your performance.

This way, what you're putting on the table is clear and the employer is given a counter offer to hire you. Plus, depending on how you explained this to them, they may see you've more value because you know what you're looking for and you're not afraid to work.

Half the time now, I hear friends who tell me too many graduates are only looking for the big figure when joining but aren't prepared to work for th big figure.

I suppose that's where miscommunication of expectations were made - during interview.