Imagine if you had hired a designer to do some new business cards and it turned out they had chosen a design from Vistaprint, then charged you their normal fee.
I don't suppose you would be too happy. You could have probably gone onto the VistaPrint website and chosen your own design and saved a fortune in the process. Well, sad to say, many designers are doing just that with your website.
You have asked them to design a website for you. They have then look at the designs available for say WordPress. They then set up some visuals based on that already available design. Once you have approved 'their design' they go and buy the relevant theme or template. They then install it set it up with your colours and logo, hey presto, an almost instant website. How much did those 'designers' charge you?
The chances are you could have done all that yourself, there are plenty of hosting companies that will provide you with Wordpress pre installed ready for you to go.
You hired a designer because you wanted something special to you and your company. So when a design company offers you a visual for your new website start asking for some awkward changes. Something like adding titles into boxes or over images. Change the link button so it displays with a border. What ever it is if they can't do it or try to talk you out of it start asking rather more awkward questions. If they can make the changes without fuss then they might actually have the ability to do the job properly.
The next issue with the above scenario is technical support. If they have relied on a bought in theme for the basis of your website design how much do they actually know about how it was put together? So if there is a problem maybe by something like an incompatibility brought on by a future update, will they know how to resolve it? Quite possibly not.
My advice, go to a proper website designer, one that has been doing it for years and one that specialises in bespoke design. Now I wonder who that might be...