Does memory affects UI performance?

It will depend on the load on your system.

Just because the RAM is all used doesn't mean much; as Barney said, the system will use all of the RAM as necessary.

But if it is starved for RAM and is using a lot of swap space, performance can degrade significantly.

Open Activity Monitor in the Memory pane, and when the system is lagging see what is says about:

a) Memory Pressure

b) Swap space used

If the memory pressure stays in green and the swap space is only a few MB (say, under a GB), then probably RAM is NOT the problem.

Of course, having 16GB could not have hurt, but it may be worth enquiring as to which applications are using a lot of memory.

If memory is scarce, quitting applications that are unused helps. One of the most egregious RAM users are web browsers, especially when there are lots of windows or tabs open. Close them if they are not needed. And among those, Chrome is known to be a real hog, so if it is part of the problem, consider using other browsers. Safari and Firefox are better.

it's just the memory that is being filled up. Is it expected behaviour?

Yes. The OS will use all memory available. If you haven't opened any apps, it might not be able to use it all, so it won't be full in that case.