It depends on how the specific controller deals with it, and most sellers have no idea how what they sell works, making it difficult to be certain without testing yourself (difficult to do without wasting money on parts you don't use).
Some will only limit current at all at the "max" current, but may only be able to continously handle the "rated" current; how long they'll handle the "max" current is unknown unless it lists that.
Some will allow the "max" current for a few seconds (or less) and then limit to the "rated" current. I would guess that this is the most likely operation mode for most of them...but I don't know this for certain, or for any particular brand/model.
I don't know a good way to tell, from most advertisements, which is the case for a particular controller, unless it actually states how that one works.
All of the ones I have here, of various "brands" (as much as that term applies to these things), only list a single current limit number, which they all limit to within an amp or two, so I dont' have anything I can test for you to see which way is more common among at least a limited number of them.
If this exact current limit is critical to your system, then AFAIK, any of the KunTeng / KT controllers, especially those listed in the Open Source Firmware thread(s), should limit "properly" even with the OEM firmware, and if necessary you could install the OSFW on it and get more options.
Unfortunately for us, it is difficult to get exact specifications for these things. Because it is very common for ebike parts (and other things), especially batteries, often controllers, to be given maximum ratings that are only momentary capabilities, with a much lower continuous capability, sellers often appear to think it makes a better advertisement to show the maximum ratings (the continuous ones may or may not even be listed by the seller because that may make it look "bad" and not sell as well as a "higher rated" product). Most sellers know nothing about what they sell, which makes it worse--they may even just copy their ad from someone else's, and if they run out of a product they may just get soemthing similar and sell it using the same ad.