That diagram is pretty jacked up. I've had to modify it.
You need to understand the following (if you draw out a quick diagram, it will make sense)
R motor cortex -> R pons -> decussate (pons) -> L MCP -> L cerebellum -> L SCP -> decussate (midbrain) -> R VA/VL -> R motor cortex
L spinal cord -> L ICP -> L cerebellum -> L SCP -> decussate (midbrain) -> R VA/VL -> R motor cortex
Cerebellar inputs
(1) Corticopontocerebellar pathway: Cortex projects to the ipsilateral pontine nuclei, which then decussate in the pons and project via the contralateral MCP (brachium pontis) to the contralateral cerebellum (intermediate and lateral zones). (So I believe that MCP arrow in FA is incorrect).
(2) Dorsal/ventral spinocerebellar and cuneocerebellar tracts: The cord projects to the ipsilateral cerebellum (median and lateral zones = spinocerebellum) via the ipsilateral ICP (restiform body).
Cerebellar output
(1) The cerebellum projects to the contralateral VA/VL and red nucleus via the ipsilateral SCP (brachium conjunctivum), which decussates in the midbrain. The VA/VL projects to the ipsilateral motor cortex.
These lesions give you an ipsilateral ataxia/intention tremor (explanations assume a L-sided ataxia)
(1) ICP
For example, Left ICP: input from the L body is not getting to the R cortex, which controls the L body
(2) MCP
For example, Left MCP: input from the R cortex is not getting to the L cerebellum, which projects to the R cortex, which controls the L body
(3) SCP before the decussation
For example, Left SCP before decussation: output from the L cerebellum is not getting to the R cortex, which controls the L body
(4) Cerebellum
For example, Left cerebellum: input from the R cortex (which controls the L body) is not being processed, and input from the L body is not being processed.
These lesions give you a contralateral ataxia/intention tremor
(1) Corticopontine tract
(2) Pontine nuclei
(3) SCP after decussation
