The AquaTube is available with either 8mm push-in fittings or 10mm hose barbs (at Wizard Designs, that is). The barbs displayed on their website are the 8mm push-in fittings (called "Plug&Cool") which are
absolutely incompatible to your male barbs, even if the diameter would be the same. Plug&Cool seals at the outside of the hose so you need very stiff hoses (made of PUR) like Rippchen already mentioned but with 8mm outer diameter.
I aree with Rippchens suggestions to exchange the fittings for 1/2" male barbs with G1/8" screw thread, this would probably the neatest solution. Don't ask me where to get those barbs, though...
Of course you can use the reducing couplings, too. Be sure to order the AquaTube with 10mm barbs if you want to do this. 3/8" are 9,5 mm so this may be a tight fit but you shouldn't have any problems with leakage.