There are three common ways to layout a web page. These include Frames, Tables, and CSS. Frames should not be used. I happen to like frames and several of my early sites were built with frames. However they are not the right thing to do.
Tables should not be used. Tables were the only way to handle layout prior to CSS. Many people that started designing in 1997 or 1998 used Tables. Unfortunately many of them never bothered to learn CSS positioning which came out around 1999. Granted tables are better for some things. Granted browsers were slow to support CSS. But browser support has not been a real issue for several years. Many who use tables may rationalize their use. This does not make it the right thing to do.
The correct and current way to design a site is with CSS - Cascading Style Sheets. Using CSS is not harder than the other methods and is more powerful.
How can you tell if your web designer is doing it the correct way. This is difficult to determine unless you can read source code. You could look at a web site that they have done. Then right click on the page to bring up the source code. Then scroll down and see if you see a bunch of
< td >
things on the page. This will tell you they are using tables. The other way is to go to a web page they have done. Go to Edit > Select All > Edit > Copy. Then paste that into a Word Document. If they used tables, you will see all the boxes show up.