I agree with others that the most common cause of this problem is a bent derailleur hanger. And other common causes are improper cable routing at the rear derailleur. Be sure that the cable is on the correct side of the pinch bolt and that the short housing loop is an acceptable length. Standard length is about 12 - 12.5 inches. A shorter housing can cause excess friction on the cable. Also check the entire cable route for anything that could cause abnormal friction or binding, like a kink.
More information may help diagnose the problem. Are we to assume that this is a 9-speed system (9 rear cogs)?
I'm curious as to why the LBS replaced the mountain type derailleur, Deore, with a road type, Tiagra. What are the sizes of the smallest and largest cassette cogs 27-27, 11-32, 12-34, other?