Flavor text tends to generalize a bit - basically the draconic influence may tug at you sometimes, but you are still you. Personally, I interpret this to mean that the majority or at least a sizable minority of NPC dragon disciples are of their progenitors' alignment or close to it - i.e. in a game a red dragon disciple would probably be NE, CE or CN unless there is a particular reason for her not to be (as in, as a DM I think it would be cool, prove a point etc).
It's a bit like with tieflings and aasimars - most of them tend to evil or good respectively, but not all of them have to follow the alignment of their outsider forefather, and some expressly go against it.
PCs can feel those urges at times as way to RP, but don't have to accept them or base their behavior on them. Perhaps you have an odd fascination with violence and death by fire - you know they are wrong, and it is shameful and disturbing, but some part of you enjoys it. You can embrace it, try to ignore it, or even go out of your way to fight it to prove (to others and yourself) you are your own person and not a mindless slave to a gene implanted in you generations ago.