Lugi, when you arrive at Atlanta the process is...
1. US Immigration. Passport check, photo and fingerprinting. Up to 1 hour.
2. Collect baggage and go through US Customs. 10-20 minutes unless Customs stop you for a search.
3. Recheck baggage for your onward flight. 10-20 minutes.
4. Security check. Up to 1 hour.
5. Change terminals. This is by an underground tram... very quick. 10 minutes.
6. Walk to gate. 5 - 15 minutes, unless you stop by a shop.
When you land in Miami you don't go through any more formalities... just collect your bags and go. Make sure you know your baggage carousel number as you leave the aircraft, (it will often be announced on the pa... otherwise look for sign as you get off the plane) because flight numbers are not displayed on the carousels
Have a great holiday!