How does the IC design process work?
Actual logic gates are designed at manufacturer's foundry. They design various gates and other logic elements within their node capabilities, "qualify" their gates, and offer several variants of libraries, for different grade of silicons, low-power, normal, high-performance, etc. So one can say this is "bottom-up".

A customer of a fab (a fabless IC company) designs top-down, from marketing specifications, down to desired functions, integrating various IPs (frequently acquired from big design houses as Synopsis), using an hierarchy of design languages (C#, System Verilog, down to Verilog and VHDL). Then they translate the RTL into offered libraries of a particular FAB. 

I hope this answers the original OP question