I think it depends on the Tigers. I had a school of about 12 that would constantly eat my plants ( didn't matter which ones! ) then also they ate the paint off 2 of my decor ( yes, I witnessed it ) and have seen them eat the small MTS snails ( no loss there, I was fine with that ) then after about a year ( they were huge, bodies almost the size of 1/2 dollars, I'm NOT kidding! ) they started killing everything in my tank ( mostly the tetras ) so I rehomed all of them to my lfs. The manager of the lfs took them all home for himself and said they were the "nicest" barbs he had ever seen! I said, "good riddance"
It may have something you do with diet. Barbs need veggies in addition to proteins so they may eat plants if they aren't being fed veggies foods???
My barbs will eat snails as well....though I finally have some ramshorns breeding in their tank without being eaten! They have even killed off all but one of my nerites (I had a dozen hitchhike on some wood).
I have 8 in my planted tank and they pick on pretty much every plant in there but they haven't ever just completely destroyed one in my experience. They spend most of their time chasing each other around and swimming through the plants not eating them.
I'm not sure about the tiger barb but my Congo Tetra will eat plants every now and then but it is never my Anubias or Java Ferns. Those two plants like most slower growing plants are darker and tougher than your faster growing plants. Most of the plants that get eaten by fish are faster growing plants so you should be perfectly fine with both Anubias and Java Ferns.