You don't need to follow Tarzan anywhere. I am not sure exactly which area you fell into, but your goal should be to get to a place called "Camp" and enter the tent to progress the next story point.
To help you more specifically, I can give you some directions.
Assuming you are starting right from when you arrive in the world:
-After you beat Sabor (the big mean cat) and get Tarzan in your party, you should be at the tree house (the wooden house).
-Follow the balcony that wraps around the tree house to the right. It eventually leads you to a ramp down into the jungle. Alternatively, you can jump off the balcony onto a rope walkway beneath the tree house and head to the right that way into the next zone.
-This area should look very green, with a central mossy tree of sorts growing up out of the center (there should also be a blue trinity mark on the ground at your feet). Jump down off the ledge you are on, and head to the northwest side of the room. There should be a high ledge here you can jump up to. It can be a bit of a tricky jump, but aim for the part that dips down so you can grab and pull yourself up. Enter the hole here to the next area.
-This area is very small and circular. There should be a well-hidden green trinity on the ground here as well. You want to find the exit out of this place which, from where you entered, should be up and to the left slightly.
-The next area should put you on a high ledge with a large open tree trunk next to a save spot. Jump into the tree. This will take you to a sort of mini-game where you have to slide along a tree branch and either jump or attack branches out of the way. It turns into a more elaborate mini game later, but for now it is just a way to travel. If you enjoy it, come back after you clear the world to earn some fun prizes.
-The tree sliding mini game should dump you into the area called "Camp". Here all you need to do is enter the tent that is on the right side, near the flagpole.
ALTERNATIVELY (a slightly less complicated route...)
-starting from the tree house again, head to the right until you get to the ramp and down into the next area.
-From here, instead of jumping up to the high ledge on the left side of the room, jump off to the left and look around on the ground there for a bright green vine coming out of a pit. Jump into that pit, or climb the vine down.
-This will take you to an area full of swinging vines and platforms. Simply jump off here.
-You will fall into a watery area with some hippos. Look for the hippo that is sinking up and down slowly, turn the camera so that he is on your LEFT and swim towards shore. Once you reach firm ground, you will have to jump across another hippo to get to the other side. In front of you here should be a vine going up, and a path to the left. Go left.
-You should be at the camp again.
Once you activate the cut scene in the tent, talk to Jane to get your next objective.
Deep Jungle has a few moments where the next objective location is slightly...unclear and it can be quite easy to get lost, so just keep poking around until you trigger something.
As a fun aside, there is something neat you can do that when it first activated for me, I thought was a glitch myself. During the initial part of the world, you may find you keep getting jumped by Sabor in random places. There is actually a small window of time where, if you return to the tree house, and Sabor is still in his "jump out and attack" phase (which does end rather quickly once you progress further in with the plot), he will actually burst through the floor of the tree house and create a hole that otherwise would not be there. If you follow the plot as it goes and never return to the tree house except when prompted, he will never do this and the floor will remain in tact. It very much scared me the first time it happened because most play throughs I just zipped through the story and didn't wander around.
Hope you can solve your dilemma and continue to enjoy the game!