First, the Coast Guard has certain unique authority over and above that of general police officers to include tribal.
Here is a link to the RCW:
http://app.leg.wa.gov/rcw/default.aspx?cite=10.92&full=true.There is a procedure set forth in that RCW whereby individual tribes may enter into a law enforcement interlocal agreement with local authorities (commonly the County). In short, the tribe(s) must provide sufficient proof of insurance and their officers must be certified.
Here is a link to the interlocal agreement between Snohomish County and the Tulalip tribe:
http://www.narf.org/nill/documents/201110snohomish-tulalip.pdf.I could find no record of an interlocal law enforcement agreement involving the Lummi tribe.
Your questions might well be the basis for a presentation by your local County law enforcement official. My questions during such a presentation would revolve around how does a non-Indian know what authority a tribal officer may have over them and how that may change depending on location. Can we demand a copy of an interlocal agreement? Call 911??
Another interesting question is if ticketed by a tribal officer (operating under an interlocal agreement) for an infraction while on a reservation and that ticketed individual wants a hearing does tribal court meet Constitutional requirements?(think Jury of Peers)