If it shifts correctly when you manually shift it the problem is either in the valve body or within the governor but since you say it starts out in first then shifts to 3rd that rules out the governor. My guess is it's possibly a weak 2-3 shift valve spring which allows it to shift into 3rd immediately after shifting into 2nd. Here's a PDF file showing the valve body. You can see the 2-3 shift valve and spring on the pic in the middle of the page