I live in Los Angeles (zone 10a) and I have just about every kind of aloe, they are probably the most successful plants in my yard. My soil is decomposed granite which is perfect for them, and of course we don't get cold enough here to have to overwinter them inside. They actually bloom in the winter!!
If it is tilting it might be leaning towards the sunlight. I would turn the pot around the other way and then it might straighten itself out. Otherwise I wouldn't be afraid to stick something under it to prop it up so it sits the way you like it. I tend to be kind of careless with them, though, since they grow so prolifically here and I am not afraid to move them around or otherwise mess with them.