A sidechain can be made to pay out bitcoin rewards to its miners, but it needs to get the coins from somewhere, as it can't generate them from thin air like the main blockchain. For example, it could get the coins from transaction fees, or demurrage (interest paid from everyone holding coins).

This is arguably a better incentive than altcoin mining since miners would be paid in real bitcoins.

The sidechain doesn't have mining. It has "trusted functionaries". Or so the white paper seems to say.