Welcome to the boards.
Specializations are not automatically raised when the skill level is increased. I am guessing that during game development it was assumed that players would focus on developing their specialization over general skill.
Very few characters should have skill levels on par with their specialization levels. As someone once posted your character may be one kick-ass pilot, but it is unlikely that he would also be a great tactical or sensory officer too. Generally, only flag (or the most experienced of senior) officers might be allowed skill levels on par with their specialization levels.
One way to avoid this problem of Skill vs. Specialization is the house rule: Specialization skills must be two points higher than the skill level before raising the skill level is allowed. Thus a Security Officer with Shipboard Systems (Tactical) 1 (2) must have Shipboard Systems (Tactical) 1 (3) before being allowed to increase his skill level to 2.
Steven "redwood973" Wood
"Man does not fail. He gives up trying."