We've used the self-cleaning feature fairly regularly on about three different stoves, and never had one in which any exterior surfaces got hot enough to be a concern. The ones with which we used it were self-standing models that sat out in the middle of the room, and weren't tightly encased in cabinetry; but in general if properly installed I wouldn't see a real hazard with them.
There are two kinds, and how you use it might be affected by which kind you have. Unfortunately the User's Manual often doesn't tell you which kind a given stove is.
The "lower temperature" kind uses a catalytic coating on the internal surfaces, so that any crud is oxidized at a somewhat lower temperature. The temperature actually used for a catalytic cleaning usually isn't really significantly lower than for the other kind.
The more common kind is simply called a "pyrolytic" oven, and relies entirely on "burning off" all the grease with high temperature. Most ovens can achieve about 500 F (293 C) for cooking purposes (a good Pizza oven temperature), and the "cleaning cycle" generally doesn't go much beyond that, perhaps 50 F (28 C) higher.
At about 500 F, if you open the door so that you let a little fresh air in, and toss a piece of paper in and shut the door quickly, the paper might "explode in flame," but as long as no fresh air is admitted the cleaning cycle automatically reduces the oxygen inside the oven (by burning off - oxidizing - a little surface grease before the oven gets fully heated) to where there should be almost no visible smoke and no flame.
The oven door must "lock shut" when you start a cleaning, and should remain locked until the oven cools down to near room temperature. You should not be able to open the door until it's cooled, so you should never see a "flame."
With either kind, any grease in the oven should be reduced to a "soft ash" and you still should (the book says) wipe that out when the cleaning is done and things cool down. It depends on how fussy you are.
In the US, it is generally required that a "professional" installer must leave a copy of the installation instructions with the new owner, so it should be fairly easy to check whether it looks like the instructions were followed. (State and local rules may vary on this.) Properly installed, as specified by the manufacturer, and operated according to instructions, there should be no particular hazard associated with the automatic cleaning cycle.
A DIY installation by an amateur, or installation of a "used" stove where the paperwork is missing, might merit a little extra caution, but the requirements to do it right really aren't all that complex.