My boys have taken Omega3 supplements since they were 3 years old. I notice a huge difference.
However, research is inconclusive with regards to whether supplements are having the same good effect as "real" fatty fish. So in addition to the supplements, I am giving them a lot of fish. Smoked salmon, mackerel in tomato, tuna, halibut, etc. This is balanced by the good fat in nuts, almonds, avocado, that I also give them, as omega3 and plant oils work well together.
I have read some research saying one should be careful with taking too many omega3 supplements, as they still had not found a natural way of preventing the oil from going rancid, and there was concerns that us humans would build up oil that goes rancid in our own fat reserves under our skin, ie, the opposite of antioxidants. Which is why it would be best to eat the natural sources of omega 3.
Now that my 8 year old is happy to eat the natural sources of omega3, I am cutting down his supplements. Will get there with my 5 year old soon, I hope.
For now, I think you should follow the advice you have been given, but at the same time try to increase his oily fish intake.