Hi Gary C and welcome to the Q&A Board!
Yep, you're right. The Minolta A200 and the Minolta 3600 HS flash unit are compatible. You did mention that you are shooting completely automatically, yes? Therefore, I would expect reasonably proper exposures. Some blowout of reflective components could happen but I wouldn't think you'd get totally blown (too bright), "badly overexposed" images. My guess is that there's something not quite right in the settings. You've probably already double-checked them. Hmmmmm, have you tried contacting Minolta support? (
http://www.konicaminoltaeurope.com/support/pi_customer.html) They may be able to help with your specific combination of camera and flash unit. Sorry I can't be of more help.

Also, perhaps other readers of this post will be able to give some insight.
