Barrel adjuster on front and rear derailleur

Hi guys,

This is my first post and I hope it's the right section. I'm a beginner and I just bought a Diamondback Response Comp 09. Before I can bring the bike home it stayed overnight at the store so their bike mechanic can tune it. When I brought it home I found that shifting gears wasn't as smooth as I wanted so I started looking thru youtube about adjusting the derailleurs.

My question is my barrel adjuster for the rear derailleur is located on the shifter not on the rear so I'm not sure if this is ok or it was built wrong? I didn't get a chance to check the front derailleur but I know I saw the barrel adjuster on the shifter as well. What's the best thing to do in this case? Should I just leave it alone or put the barrel adjuster on the correct place, or does it work either way??

Any information is greatly appreciated. Thanks in advance.