While the barbed connector fittings are capable of 125 Psi water pressure, they are not very strong structurally, and excessive force when pushing the tube onto the barbs can easily break them. They are not expensive, and we will gladly ship some more off to you in an envelope, but to push the tube onto the barb correctly there are two ways.
9 times out of 10 if someone complains about the tube coming off the barbed fittings under pressure, it is either because the tube has been overheated (in a flame) before being pushed over the barb, or because the tube has not been pushed all the way over the barb.
The easiest way is to cut the tube off straight with sharp scissors, and to pass the tip of the tube through hot water or an open flame for just a second. Not any longer. This will cause the tip to be slightly softened up, making it easy to slip over the barbs. It is VERY important not to over-heat the tube end. It takes a little practice, but essentially, the shorter time in the hot water or the flame you can get away with, the better. If you realise that you did hold it in the heat for too long, or a joint pops off under pressure, just trim the tube end half an inch back and do it again. The polyurethane tube is flexible and stretchy, but this does underline the need to leave a little slack in your tube layout until you gain enough experience.
There is also a Pincher Tool you can make yourself. This will allow you to push the tube over without any heat. Check out Q18 for details.