Sounds like he is fobbing you off, no way a seal needs to bed in!
Stupid question but it is water and not oil, there is a standard rubber seal that seals the gearbox which sits behind the mechanical seal.
The water pump seal has three parts, the metal body that sits inside the case, a flat seal that presses into the back of the impeller itself and the main seal with the spring in it. The main seal seals against the metal body and the rotating impeller, the spring puts pressure on to the part of the seal that mates with the impeller (this is hard to explain but is quite obvious if you are looking at the parts)
The only part of the impeller shaft that has to seal is the section that runs in the gearbox oil seal, if you have oil not water leaking then it is either this shaft or the oil seal that is the problem.
The area of the shaft that normally corrodes is the part that sits inside the mechanical seal, if it is corroded I would say it is a sign that the seal has been leaking previously.
If it is definetely water coming through the hole it must be either the seal is damaged ( unlikely if it is a new seal) the flat seal that presses into the back of the impeller is either damaged, was damaged previously or is not seated correctly ( on the piss) in the back of the impeller or the metal body has not been replaced and was damaged/worn previously or the new part has been damaged on installation.
From my previous experience of changing these my money would be on the metal body being damaged on instalation, this part is thin gauge sheet metal and actually quite delicate, it only needs some monkey hitting it a bit to enthusiastically to knacker it. I speak from experience
Either way I would be having a word with the guy who changed it.