Tiger barbs are egg scattering fish, which means they usually scatter their eggs within thickets of plants and across aquarium gravel. In my experience with most barbs, they'll need to be well fed a high protein diet and you'll have to do a lot of water changes to encourage them to spawn. Lots of water changes with fresh warm water will help simulate rainy seasons where they are native to and an increase in live foods like daphnia, brine shrimp and worm meat can get them into spawning condition. From there, expect spawning to occur at any time but chiefly before dawn or at dusk.
Tetras are exceptional advantageous omnivores, so they definitely will go after their own (or tankmates) eggs. You'll have to do a little more research in how to separate the eggs from the adults during spawning.