If you are referring to your first Contact Check ride in either the Tweet or 38 then the answer is NO because those are UPT Cat check rides not Form 8 check rides. Now the time that your were solo in the Tweet (i.e. 7-9 hours counts as PIC) and the time you were solo in the 38 (15-22 hours)
If you have Tweet or 38 time after UPT (Instructor Time) then you have another ball of wax to deal with for the FAR interpretation of sole manipulator of the controls because of the time you might have flown with another Instructor.
But, make sure you do include that time from UPT in your total time
Like BDGERJMN said if something happen to the jet who would get in trouble you or the IP!!!