Yes and no.
There are two kinds of civil infractions - traffic and non-traffic. "Traffic" basically means that your violation is part of the motor vehicle code. "Traffic" does not mean moving or non-moving.
A speeding ticket is a moving offense; a tabs violation is non-moving. However, both are properly marked "traffic." Why? Because if you read the notice of infraction you were given, you'll read under "traffic" that you can't be arrested for failing to respond (although your license can be suspended, which can lead to all sorts of problems).
With a non-traffic civil infraction, however, you can be arrested for failing to respond and charged with the crime of failing to respond to a notice of civil infraction. Again if you read your notice (ticket), you'll see that language on there. The "traffic" and "non-traffic" boxes simply put you on notice of which example applies to you in the event that you fail to respond. It also helps the State of Washington keep track of traffic and non-traffic civil infractions for statistical purposes, which is important for the allocation of public funds for courts and roads.
So while a tabs violation will not affect your insurance premiums, it will go on a full abstract of driving record - but again, it really doesn't have an effect on you, provided you don't ignore the ticket. A speeding ticket or other type of moving violation (e.g., failure to yield, negligent driving, improper lane change, etc.) would have an effect on your driving privilege and your insurance premiums.
Incidentally, if you will promptly get the proper tabs and show that you have obtained the tabs, the court will likely significantly reduce your fines.