Sounds like your phone rep was a bit confused. Gig is indeed delivered over coax. In some areas, gig internet does require a professional install though. There is no reason you can't go ahead and self-install your modem. I don't know if they will move you to the gig tier tho w/o a tech visit.
All you need to do is physically swap your new device for the old. Once your gateway is online (watch the lights), connect your computer and open a web browser. It will take you to an activation page. You'll want to have your account number and phone number associated with the account handy. If everything goes smoothly, the whole process should take about 5 -10 minutes. If you have issues, call.
1-800-COMCAST (1-800-266-2278) or 1-800-XFINITY (1-800-934-6489)
Eh, if everything is working fine, there is no reason to have a tech visit. I wouldn't trust that they won't charge you an install fee. Glad you got it activated!