The river vines alternate between being up and being down. When they're up and above the water, they'll grab you when you jump. When they're down, you can cross.
If you really can't tell which state they're in... jump, see what happens and make note of which one of the two states the vines were in. If you make it successfully, great, do that again. If you get caught... then do the opposite.
Not sure what else to say. I feel like it's fairly obvious...? But I also helped make and test the game, so of course I know what's up.