Rapid expansion is favored for all civs. I'm not sure Tleilaxu are particularly better at it. The +1 shrine gold from an extra city is pretty small in the big scheme of things.
Yes, settling prophets (I wish we could make them Tleilaxu Masters) is the intended strategy for Tleilaxu, and yes this gold can give a nice gold boost.
But they need it, because they'll have a lot of difficult getting anyone to trade techs or resources with them, and they're much more likely to be dogpiled.
I would consider removing the Philosophical trait though and finding a substitute, but then the Industrious guy would be a no-brainer.
The free GPP from the palace was really needed in order to help the AI get the shrine early, and actually start building a priest economy.
Any particular suggested changes, or ways we could weaken them in human hands without penalizing the AI?
AI Tleilaxu feel about right, its human Tleilaxu whose economy that can be problematic.