Welcome to TFF.
I would not recommend adding different species here, as there are some issues with what you have that should be handled first.
The tetras and barbs are what we term shoaling fish. These fish live in groups of hundreds, even thousands, and they have an inherent need for several of their own species programmed into their DNA. "Minimum" numbers are sometimes necessary to avoid overstocking tanks, but with shoaling fish the more there are of the species the better, generally.
When the numbers are not sufficient to satisfy the temperament of the fish, they react. Usually this is with increased aggression. Feisty fish (like the Black Skirt Tetra) will tend to become much more aggressive, while normally peaceful fish will tend to become somewhat aggressive. This is believed to be the fish's only response to frustration. The green citation in my signature block is referring to this aspect.
Six is the minimum, but a few more would be even better for the tetras. However, this brings us to another issue, the tank size and water volume. This species will grow to 2.5 inches, with some sources giving 3 inches. A group of this species will fill the 20g.
The Rosy Barbs also need a group, but this is not going to work in a 20g. This fish will easily reach 3 inches, and 5-6 inches is not unknown. They need a lot more room, at least a 3-foot tank but I would not put them in less than a 4-foot. I suggest you consider returning the two barbs.
Everything may seem peaceful now, but it is early days. The fish are in a new environment, and different fish settle differently. The stress of being netted and moved was significant, and they need to recover, so they are often on their best behaviour out of anxiety more than anything. But this will likely change. We can only assume that fish will behave normally for the species, and plan accordingly. Now is the time to make changes for the good of the fish; later may be too late, as once fish are stressed by insufficient numbers, inadequate space, etc, the internal ramification is done and they don't turn back. Stress that becomes severe will cause health problems, weakened fish, and premature death (meaning, not living to its normal lifespan).
Byron.
