Freewheel is not making noises
Based on your symptom of the 'rear wheel being versatile" which I take to mean a wobble related to loose bearing adjustment in the hub. If the mechanic completed a complete hub overhaul the axel, bearings and cone nuts would've been removed, examined, replaced if needed and then put back together packed with new grease and adjusted properly so that the wobble was gone.  None of this takes place where the "clicking" is generated. However I often try to get some lubrication dripped into the freehub where the pawls engage to create the drive force of the sprocket. A combination of lubricant and a tighter bearing system can sometimes quiet the pawls. Other times the sound is more distinct as the liquid lubricant loosens the old grease and the pawls move more freely and "snap" through their range of motion.  Obviously there may be something wrong if you're experiencing a slipping sensation or if when you begin pedalling again after coasting there's a sensation of the cranks free spinning and a delay in the normal resistance to pedalling.