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.
I don't believe he'll be fired immediately. Xabi is a very successful coach, and if his Real Madrid career progresses normally, it could last a few years. Spain is a place he knows well, and he's a coach who's attuned to young players. I still remember what he did at Leverkusen. They didn't lose a single Bundesliga loss for an entire season and reached the UEL final. I have full confidence they'll do the same with Real.
But why will the club wants Xabi Alonso transferred out of the club when he's gotten a good.tract records with his performance so far. This season the Real Madrid team has played two games, one with Osasuna which ended in a goal to none and the other with Oviedo which ended with 3 goals to none. The club is still at the third position not because of their wins but because of the goal advantage which is nothing yet. The club still got a lot of games to play with one against Mallorca and Real Sociedad in their subsequent games which many of us will agree is mostly likely in favour of Real Madrid. What I cannot guarantee Xabi is whether he will be able to recreate his unbeaten winning streak in a league like LaLiga but I know to keep such records will be very tasking.