You are right that they are in rebuilding phase which is tough for team with such high expectations. Xabi Alonso has to win games and he builds team because if they start losing he could quickly be fired. You are also right that real test will be how they perform against big rivals like Barcelona and Atletico Madrid as those matches will truly show how much team has improved. For now they are doing well enough to give them time they need to get better.
In fact, Xabi Alonso, who doesn't even have much coaching experience, will certainly have a bit of a struggle at first when he becomes the coach of a big and most famous team in Europe, Real Madrid. The pressure he feels will certainly be enormous, unlike the two previous clubs he coached, Real Sociedad B and Bayern Leverkusen. But so far, Xabi Alonso has immediately shown positive things, although some matches have not gone as smoothly as expected. But the most important thing is that this team is starting to improve, even if it is slowly. And indeed, the real challenge comes when this team has to face rival teams like Barcelona and Atletico Madrid, who always compete fiercely every season.