Not completely familiar with the vented systems expect from this form. I do understand your concern. If the original vessel was used and designed for use with an open/vented system and now say you have 40-50 psi in it could be a major safety issue. Not knowing if your plumber did his research or not, it is very hard to say if it is safe or not. In a unvented system there should be an expansion tank, and a safety relief valve. Also the tank would need to be rated for the pressure. Copper tanks can be rated to handle this but that doesn't mean you tank can. Look on you tank to see if you can find a rating or manufacture tag. If you just find a manufacture tag with a model number or something try and contact them. I guess do a little homework to try and see if it is able to handle it. I don't know what leval of water presser you have, I was referring to the 40-50 psi as that is common in my area.
some info on vented and non vented