My Quartus designs typically have three files:
o DESIGN.qpf ... the Quartus Project File, which just sets the project revision
o DESIGN.qsf ... the Quartus Settings File, which has most of the Quartus "set_xxx ..." commands
and
o DESIGN.sdc ... the Synopsys Design Constraints file, which has timing related commands like
create_clock, set_input_delay, set_false_path, etc
Each of the tools (quartus_map, quartus_fit, quartus_asm, quartus_sta, quartus_eda) have access to all
of the above files via the DESIGN.qpf/qsf/sdc file(s), so theoretically each tool can use any file contents
as it sees fit.