While using TIBCO ActiveMatrix BusinessWorks Plug-in for Oracle Tuxedo 6.1.0, it is OK to install 64 bit Tuxedo Client to communicate with 32-bit tuxedo server.
There is one exception from Oralce as below:

Interoperability of 64-Bit Tuxedo 10gR3 Workstation Client With 32-Bit Tuxedo 10gR3 Server ( Doc ID 1299575.1 )

64-bit Tuxedo WorkStation client is supported to communicate with 32-bit Tuxedo WSL/WSH server with one EXCEPTION.
If there is a long field in a Tuxedo VIEW(32) or FML(32), with a value greater than MAXLONG32, the whole message cannot be transferred between WSC & WSL/WSH.

The reason behind this is Tuxedo uses the operating system provided xdr_long() functions to encode "long" types, which can only handle 32-bit even in 64-bit platform, to keep the compatibility to 32-bit operating system communication(across the network).