So they're only expecting a reaction from the Pfizer not the other?
Early on there were a couple of reported cases of anaphylaxis after receiving the Pfizer vaccine, so it was made a requirement that patients need to be observed for 15 minutes in case they have this reaction.
It has not been observed as a side-effect of the AstraZeneca vaccine, so that does not have the same requirement.
Which is fortunate as if everyone had to wait it would limit how many vaccinations you can give to the size of the waiting room. But as it is potentially fatal you cannot ignore the risk with the Pfizer vaccine.