Unlock Phone

I bought a new phone (2 phones actually) through T Mobile then decided their service wasn't for me. I switched back to VZW yesterday only to find that the phone won't work because I hadn't paid it off yet. Makes sense, I paid it off through T Mobile immediately. They said they need to send a request to Apple to unlock the phone. I am dead in the water waiting on this to happen. Does it normally take longer than 24 hours to complete this? And will they do this over a weekend? Also, once I get the email, is it as simple as popping the new SIM card in and away I go? I am a bit impatient but we can't use our phones until we get them unlocked. Just trying to keep ahead of this so I can get back in business.