You're not talking about the first rental payment, you're talking about an incentive to hold the apartment, that you're serious about your offer. Doesn't have to be much, I'd think $1000 pesos or so (that's how much I put down on my apartment when I made my offer, they might ask for 10% of the first month or something like that). That shouldn't happen until you have made an offer to rent the apartment.
And also, I'm talking long-term rentals here - there shouldn't be any "offer deposit" for temporary rentals.
If the owner accepts your offer and you back out, the owner keeps your deposit. If the owner doesn't accept your offer, you get the deposit back (don't let them tell you otherwise). If you both go forward, the money you put down goes toward your "closing" costs (like IVA, for example).
If they tell you anything else about that deposit, you should tell them you know better, and if they continue, go find another place.
When you close on the apartment, you have to have the money for the security deposit and the first month rent and the commission for the rental agency, plus IVA (I believe IVA is only calculated on the commission though, not the rental payment or the deposit). When you go to sign the contract, they should read the contract aloud at the rental agency's office (at Remax they had a projector and we all followed along, otherwise you'll follow along on your copy of the contract) and assuming everyone is happy, you'll all sign the contract and money will change hands. That is also the point that the owners give you the keys.
Remember, everything I've discussed above is for long term stuff. Just to make sure (sorry if you've already mentioned it or it's something obvious to you already) - do you have a property guarantee, or have the owners said they will not require a guarantee? Usually the guarantee is something the rental agency will ask you about before they will even talk to you about showing you a property, but sometimes they just assume you know the situation (although not very often assumed with foreigners).