A little background on the blown fuse.
The instrument was almost unused, bought new a couple of montgs before.
I was probing inside a chassis and accidentally touched the 220v and poof! it blew. quite a bang actually, those fuses dont go quietly,
The internal fuse is a 12A slow ceramic, the rear fuse a fast 10A. makes absolutley no sense that the internal should blow before the rear fuse.
This is the one and only fuse I have had to replace on this instrument.
Do you have still available data how these fuses was marked... All markings what can find in one fuse end or how ever they have marked voltage, current and speed class. Example (F 10A 250V) or how ever they are.
Also, it need note that some glass fuses 5x20mm have really very low interrupt rating what may reach quite easy in total short circuit (depending source impedande)
Then over current - time - break curves can be really unpredictable, there may be really wide tolerances. In one manufacture lot one 10A fuse may break after 10s 15A but and 1s 25A and 0.1s 60A and 0.01s perhaps 200A and 0.001s perhaps 1000A. And then, min and max curves may differ really lot.
Of course these depends fuse type. But fast or ultra fast and slow fuses have not very big difference in some circumstances in practice even if I2t is many fold.
Some 5x20 glass fuse may have as low as 35A - 100A interrupt rating. (means that if current is more big it can not break in worst cases, example Littelfuse type 218 <4A and example 10A have 100A interrupt rating and some other type have 10kA)
If really want build, using fuses, even some kind of circuit (passive) component protection it really need do lot of study and tests and very extremely carefully and clever select fuses. Mostly no one do it seriously. And it can understand because result is still poor or just borderline And still not for usual semiconductors.
Fuse is, as nctnico told, more like preventing fire etc. (as told, of course also some amount circuit protection. But as can see if really look fuses true data... 10A fuse make still over 1000A short peak possible.
Why internal 12A blow and not external 10A. There may be several and also natural reason. One reason may be fuses tolerances in over current time curves. It can be very possible that if short circuit current is example 50A first blow 12A and after it blow 10A is still ok condition if both are not in they tolerances middle ones.. if other is from other side and other is from other side of normal distribution it is very possible even if external 10A is F(ast) and internal 12A fuse is T(race)
Even if there is example under 10A fuse (yes it can and 10A not continuous measurement is possible)
There can be still very high maximum short circuit current (if source can feed it). In this game it do not mean lot if short maximum is reduced by fuse to 200A instead of 250A or how ever it is)
Here one tiny example about time current curve (average - and it mean that every fuse have min and max curve and area between these are big.)
But then, here is just ONE example about one type min and max curves. All fuses have different these curves. This may give some imagine how tolerances may affect and give one possible explanation also for this case. As can see differences in min and max is huge.