No. With only a few, very narrow exceptions, Washington workers age 16 and older must be paid a minimum wage of $9.19 per hour. I am aware of no technicality that would allow employers to reduce the hourly wage of workers who are late reporting for duty. If the employer does not approve of the employees' work habits (for example, showing up late), then it is free to discipline or terminate the employment of any such worker. It may not, however, pay less than the statutory minimum wage as a punishment for tardiness.
Refer to 49.46.020; see also WA Labor & Industries website at http://www.lni.wa.gov/workplacerights/
Good luck to you.
This does not constitute legal advice. You should consult an attorney who can assess the facts of your case and discuss your legal rights and obligations.