How to change Warp effect on a text layer to same effect as in Illustrator?

You could do it without precomping the text layer and solid with Compound Arithmetic and Wave Warp, but it involves a bit of set up.

Start with your text layer with some sample text.  For Compound Arithmetic to work right, we'll need the text to be positioned in the upper-right corner of the comp.  To make sure it stays there, set the position to 0,0 and then add this expression to it's anchor point:

rect = sourceRectAtTime() ;
[ rect.left, rect.top ]

To make things easier in the next step, change the name of the text layer to MyText.

Now create a 1x1 solid (1px by 1px) and add the Repetile effect and then add this expression to the Left and Right properties:

target = thisComp.layer("MyText") ;
target.sourceRectAtTime().width / 2

And add this one to the Up and Down properties: 

target = thisComp.layer("MyText") ;
target.sourceRectAtTime().width / 2

That should make the solid the same size as the text layer no matter what you type in it.

Now add the Compound Arithemtic effect to the solid and set the Source property to MyText and the Operate On Channels to "ARGB".  Your text should now be composited on the solid layer.

Now add the Wave Warp effect to the soild, set Pinning to "All Edges" and set the other settings as desired and the Wave Warp should be simlar to what you can do in Illustrator.  When you update the text in the text layer, it should update the text on the solid and the size of the solid whild maintaining a consistent Wave Warp with all edges pinned.

Thanks! Yeh, I made few fast tries with those effects, although it seemed a bit weird that the "warp" effects ( ones I used ) differ like that between the programs. So, there's more interest towards getting the same effect (and if possible, how) done with the warp rather than tweaking it with other tools. Although there's also time limit with the project so I mostly like will follow up your advice, thank you 🙂 But out of interest towards solving the problem with the warp -effects, I would like to learn if its possible to be done somehow.