Hi, please note that in Corona Renderer the animation modes have no effect. It works always as using the "Following" mode, because the items are instances of the scene object, and follow its animation.
You can see the compatibility list here
Said that, in this case it should work because you are using exactly that mode.
The problem is that movement, rotation and scale keys are not recorded by Forest because are not part of the object, but of its transformation. You must use the following workaround:
1) Take the original mesh object used for the proxy.
2) Create a Helper->Dummy object and animate it (adding the movement keys).
3) Add a "Linked XForm" modified to the geometry, and pick the Dummy as Control Object.
4) Assign the geometry to Forest as usual.
That's all. I suggest to use standard meshes with Forest, because usually proxies don't add any benefit. But if you want to use a proxy, these steps are optional:
4) Convert the geomety to a proxy. The movement produced by the Linked XForm will be embedded within the proxy's file.
5) Use the proxy with Forest.
I hope that helps.