the 2003 civic had the electronic gearbox, it learns the shift pressure as you drive; and a used gearbox will feel sloppy when the ECU has been reset of all shift adaptations.
Mechanic probably disconnected the battery.
Keep on driving it and see if it adapts. if it fails to adapt then you have to overhaul it - Honda make garbage automatic gearboxes - you wont be the first to experience this.
If its a hydraulic box (e.g. someone put an older civic box in it) - then you can adjust the pressure cable to firm up the shifts - the old honda hydraulic boxes take dexron III and have very firm shifts (they shift very hard/strong/bump) - if you fill such a gearbox with the new DW1 or Z1 oil it will feel like its slipping when catching a gear.