For me it seem to be a hit and miss. As an example, I had one of my crime families order a pizza (they live in Oasis, the same street as the Calientes' live if that matters) and I had to call two times for it. The first time I got no notfication or any acknowledgements that they had ordered a pizza and the pizza was not there 2 Sim hours later.
Ordered again, got the notification and the pizza girl arrived shortly after that (I didn't take note on how much Sim time it took her though). She even stayed around and played chess with one of the kids (not autonomous though, I had the kid invite the pizza girl to play via the chessboard as an experiment). She stuck around for one game and then she took her money and left.
Other times it has happened that I have not gotten notification and no pizza and then other times I get the pizza. I am starting to order the pizza a second time now if I don't get any notification the first time around.