I agree with CyF16. I am confused if you took it in for a valve job he would only need to remove the head. I have an '87 MKIII with the 7M-GE engine non turbo. I took the head off and took it to a shop that only did valve jobs. I had no problems.
There could be possibilty that he drained the oil and then ran the engine with out oil? If he is professionsal mechanic you should not be having problems. I am a car hobbyist. I learned the basics about auto mechanics taking a course as an elective while in high school over forty years ago. I have done some major work for myself, friends and acquaintances. If you have good hands on skills and you can read and understand manuals you do can a lot. However, the Supra has complex engine with computerized control and a very complex electrical system and vacuum system. As do almost all cars these days.
You need to find an experienced Supra mechanic. I noticed one of the replies you received is from professional mechanic. You problably have not had time to see if the valves adjusted correctly. Once your friend? mechanic confirms he has done it correctly. That may solve your problem. the guy who did the valve job on the head for me was not a Supra specialist.
Dan