I cannot be totally confident as to the cause of your Dwarf Alberta Spruce tree without seeing the trees but the number one culprit for what you describe is spider mites.  The Dwarf Alberta trees are a favorite target for the mites.  To investigate take a sheet of white paper and hold it under an affected branch of the tree.  Tap the branch and you should see tiny specks moving around on the paper.  They are sucking creatures that slowly suck the plant fluid from the tree causing the needles to turn brown and eventually the tree dies.  The time to treat for them is now. 

An informative article on the mites is: https://ento.psu.edu/extension/factsheets/spruce-spider-mite

There are many products for treating spider mites available at nursery and large box stores.  Note since the mites are more closely related to spiders and ticks but not insects not all insecticide formulations are effective.  Read the label and make sure it is a miticide and that it is safe for Dwarf Alberta Spruce trees.   More than one application is probably going to be required since eggs are hatching and the spray does not affect the eggs.  The treatment must be applied over the entire tree from inside to outside on the tops and bottoms of the branches and from top down in the center of the tree.  A pump spray applicator with a long nozzle is best for reaching into the tree limbs unless the trees are too large and then a hose connected sprayer can be used.

Remember miticides are poisons and should be used carefully.  As with all treatments read the label carefully and obey all the precautions. 

Thank you for using Ask an Expert

Tony