International flights begin boarding 50-60 minutes before take-off, and so what seems like a comfortable connection may in fact be tight. My usual advice is to allow at least 2 hours, especially since there are fewer flights to most international destinations and your options for being put on the next available flight are more limited.
With 1:15, there is little room for error and if you miss the flight you'll have to wait at least another day. While you probably will make the connection, I would get an earlier flight from Miami for some more comfort.Edited: 02 October 2018, 00:40
I would want more time, especially leading into a long haul flight - not because it takes any longer necessarily, but for extra insurance against delays on the flight from MIA. If you miss your flight to JNB they will put you on the next flight with available seating, but that likely will not be until the next day (or possibly even later).
This is definitely a case where it is better to be an hour early than a minute late. As JAtlanta states, there is no margin for error with a 75 minute connection - that might be OK for a domestic departure, but I'd want 2 hours (or even more) in this case.
I assume this is all on DL and in one booking? If not, you'll definitely find yourself in a pickle.
If you arrive and leave in the same concourse, 1:15 is not too bad.
If you arrive in one concourse (A-D) and have to leave from the International concourse (F), you may miss your flight. I would advise to check your gates of your arrival and departure the day of travel. BEFORE you take off, check with a gate agent to assist with your transfer so you are better prepared for the transfer when you arrive.
The departure gate may not be known when you depart MIA and the gates are not likely to be the same ones as the day before. At any rate, the chance of it being on the same concourse as the arrival is not too high. And BTW, international concourses are both E and F.
"have to leave from the International concourse (F)"
There is no such thing as an "international concourse" at ATL, only an International Terminal (which is physically attached to Concourse F but is operationally a separate space).
As Stevedec notes, international flights normally depart from either E or F. Please learn to get the terminology right if you going to post advice here.
"As Stevedec notes, international flights normally depart from either E or F. Please learn to get the terminology right if you going to post advice here."
Stevedec didn't state international flights normally depart from either E or F (at least not in this post) but that the international concourses are E and F. Since this traveler is not driving to the international terminal, this person may have to take the train to Concourse E or F so the terminology is correct.
The traveler didn't state what airline is being used so we don't know. That's why I generalize my advice as I know that Southwest flies nonstop to Mexico from Concourse C. Besides Delta, I don't usually fly on other airlines so I don't know how they operate.
If this is one airline that gave the traveler 1:15 to change gates, the airline should be aware of the travel time from gate to gate. If it was done by a travel agent using a couple of airlines, maybe not.
Stevedec - Thanks for the correction of E and F!