When I ask Alexa for my weather it reports general weather near me and not my weather station data.
When saying “Alexa, ask WeatherLink for the current conditions”, if your Echo device gives you general nearby weather and not your weather stations actual data, it may be that Alexa did not recognize the key words it needs to hear. It must hear the words "ask WeatherLink" and "current conditions". If your station name has special characters (e.g. Tom & Marys Weather) your Echo may not retrieve the data properly. Try changing your station name, on weatherlink.com, and remove any special characters.