Technically, from the SRM FAQ:
All skill tests made during downtime are done by buying hits and using the standard rules for limited Extended Tests (cumulative -1 per test, p. 64, SR4A).
So it's not just extended tests, but all
skill tests during "downtime".
Of course, since most non-extended tests are pretty quick, most GMs will allow them to take place during a run, which is not downtime.
It might make sense that the Arcana test might take hours or days, since you're essentially linking your astral signature to that of the group, but I don't see a rule stating how long it actually takes...only that you can only make one test per month.
So it seems pretty open to GM interpretation as to whether or not this has to be a downtime test or if they can witness it. On the other hand, I suspect the downtime rule was placed to mitigate the need to witness dice rolls. Maybe the spirit of the rule is that anything the character does long-term (like this Arcana test) should be a non-witness 4:1 test...but that's speculative, of course.