If you set the import request as the parent (stays in running state while the child executes) then I think that the XYZ program won't kick-off until both of them finish execution.
Incompatible programs shuld not run at same time. I would suggest you try to submit child request manually and then try to lauch XYZ program and test.
I am not sure if there are any different rules for Request Set ( should not be different). If it is still happening raise SR