koti

Right. I would be really surprised if someone actually used the nr 2 meaning from that dictionary. But then again it might turn out that I will be in for a surprise. 

I know this is late to the party, but I would say turn up if speaking in first person. The example given in nr 2 of your link reads perfectly fine to me though. I believe the main difference is how many people you are referring to. I cannot think of an example where you would use turn out to refer to one person. Also, generally speaking there is a difference in the implication of something that is planned (as in turned out) vs something that came about unexpectedly (as in turned up), although this is not so much the case in the way you have used it here. 

That's it. It eluded me somehow that when referring to a big crowd, "turn out" is fine to use - now I realize I heard it and red it multiple times. I asked a native Canadian who teaches English and he only came up with it the next day. English is weird at times.