Communicating during an emergency is always a challenge for response workers at evey level.  The dissemination of timely and accurate information is crucial to the successful management of any event.  There are several ways you can ensure you are getting the correct local information for your family.
In the event of a potential tsunami, the entire Pacific coast of North America receives it's information from the West Coast and Alaska Tsunami Warning Centre in Palmer, Alaska.  The WCATWC was established in 1967 as a direct result of the Mar 27,1964 tsunami that impacted Port Alberni.  It is also responsible for the Atlantic coast of Canada and the US, and the Gulf of Mexico. 
When an earthquake occurs, seismic data is quickly analyzed to determine if the possibility of a tsunami exists.  If a tsunami may have been generated, sea level data, tsunami models and historical tsunami information are evaluated to estimate impact location, time and level.  The first alerts are sent usually between two and five minutes after the event occurs.  Upon receipt of this information, the priority of the AV Emergency Program is to get accurate, local messaging to the public as quickly as possible.  This process is evaluated after every event and is always improving.  You can register to receive the same messages as we do from WCATWC by email.  Go to http://wcatwc.arh.noaa.gov/?page=email .  The SMS/text is only available to US residents at this time.
For all other disasters (forest fire, major flood, chemical spill, etc) and another layer of tsunami messging, check out http://www.emergencyinfobc.gov.bc.ca/.  On the home page, there are links to their Twitter, Flickr, Pinterest and other social media feeds. 
Locally, the ACRD website and Alberni Online will have current information during a disaster event.  93.3 the Peak will also be broadcasting live whenever something happens.  A Twitter account is in the works and I'll let you know when that is up and running.
With the advent of social media, information (and misinformation) is circulated at an amazing rate.  The above sources are reliable ones you can use to monitor what's happening and be confident the information you are getting is accurate.