Hi David,
Yes each time you are using the debugger it will run the init script. To look at which init script is being used follow the below steps. Assumption is you have a project open and compiled.
Run->Debug Configurations...
Open the "CodeWarrior" folder and select the target you want to flash and debug. For me it is mfs_nandflash_twrk60d100m_Int_Flash_Debug.

Then click the "Edit..." button under Target settings to see the below picture:

Click the "Edit..." button next to the Target to see the following window to point to the init script and tab over to the .mem file selection too:

The file name is hidden but I've copied it here for one and all to see:
${ProjDirPath}/Debugger/init_kinetis.tcl
And .mem file:
${ProjDirPath}/Debugger/MK60FN1M0.mem
Regards,
David