I'll second Ringo Starr. I don't think Dukakis would have reacted much differently than Bush Sr. Bush was a moderate "Cold Warrior" compared to Reagan, and was at times heavily criticized for his lack of passion when it came to the breakup of the Soviet Union. The most infamous example of this was his "Chicken Kiev" speech in which he basically advocated the continuation of the Soviet Union.
Maybe you would get a few such "Chicken Kiev" speeches out of Dukakis, but maybe not. He would have been wary of being seen as "soft" on the USSR, so he may have been less likely to support Gorbachev towards the end. After all, unlike Bush, who had loads of foreign policy credibility, Dukakis was a neophyte when it came to foreign affairs. This would make him more likely to listen to his political/diplomatic advisors, whatever his instincts.
No idea how he might react to Tienanmen.