VMware support replied to my question.
Yes, the 10.1.0 tools version IS needed (even though 10.2.x and 10.3.x release notes do not indicate it.)
- The path to upgrade is pre 9.4.x-> 10.1.0->10.3.5.
Alternately:
- From 9.0.5 upgrade to version between ( 9.4.x and 10.0.x). Once your VMware tools is on any version between 9.4.x and 10.0.x , you can upgrade to 10.3.5.