What was the 1300 for? It should say on the contract, and it would answer this question. Normally people ask for first month, last month, and deposit at signing. However, if they're asking for pro-rated, maybe that means you didn't actually pay first month.

If you're at all concerned about this, I'd keep your receipts (which presumably will say what month they're for). They can't just randomly double-charge you for a month legally, but that doesn't mean it doesn't happen.