Troubleshooting a new shifter
I would start by looking at the shift cable and housing. The housing may be flexing too much and the cable may be sticking in the housing. This causes cable movement at the shifter to not be reproduced at the derailleur. If you are replacing the shifter it's a good idea to replace the cable and housing at the same time.   

Assuming you have a 2016 Allant 7.4. That bike came with 9 speed Acera shifters and a Deore rear derailleur. The EF65 shifter is a Tourney level component - that's at the bottom of the Shimano hierarchy. That may also be contributing to the problem. I definitely recommend going with a better shifter that matches the rest of the drivetrain.    

If your bike repair shop has spent a month trying to get this right with no success I'd also consider trying a different shop.