No, Aloe pillansii should not be doing that. Your plant must have some hybrid character. Maybe consult with wherever you bought it to get to the bottom of this... I'm guessing that whoever produced the seed did not protect the pollinated flowers from outside pollinators (usually you have to block access) and something got through.
It's important to bear in mind that this is an extremely rare aloe, which means that true seed is going to hard to find (since it requires two mature plants). That's why prices are so high for these plants.
There's no reason why your plant can't end up totally fabulous even if it suckers at the base. That would make it a little different and perhaps give it some interesting character. Almost all the aloes I grow from seed are of hybrid origin and the little surprises that show up along the way can be quite fun.
