With the JIC-File (JTAG Indirect Configuration) you can only program your FPGA Configuration File.
If you turn the power off and on again, the FPGA will only be configured.
If you want to flash your Software ELF-File from your Nios project you have to use the Nios II Flash programmer.
Start the Nios II Eclipse Software, open your project and then under the Nios II Tab, start the Flash programmer.
Under File -> New..., you can configure a new Nios II Flash Programmer Setting File.
If you have a SOPC Info File and an ELF-File you can start the programmer.
After programming, the Programm will start running after you unplug and plug your board again.