It would appear that whatever the "admonishment agreement" was indicates they will not be making a police report or seeking criminal prosecution. Don't be surprised if you receive a civil restitution demand from the store for the cost of the merchandise plus an additional penalty of up to a couple hundred dollars. Best advice is to stay away from the store and pay any demanded civil penalties promptly. If you are charged with Theft you should hire an attorney because Theft is a serious matter when it comes to your immigration status. You indicated that this may be your first offense, if so, even if charged with Theft criminally you may be able to avoid a conviction. You would want to ask your attorney if a civil compromise or diversion is viable in your particular case. Good luck!
The course of action would be to consult with a qualified attorney who has experience with theft charges in Seattle.
That being said, I have had extensive experience with theft charges in Seattle, many involving Nordstrom's, and I can say that not reporting thefts to the police and offering an "admonishment agreement" is a new policy for them and it appears to be a good one for those caught taking merchandise from their store. A client of mine recently had an experience similar to yours; signed the "admonishment agreement," paid the "civil penalty" and the matter has so far not been charged in court (it has been 2 months since the incident).
Please feel free to contact me if you wish to discuss your matter further.