Not exactly the promise.
I was referring to how both Jessie and Aerith called Cloud their 'hero' in different stances in the game ( when saved/helped by him), while here we have Tifa, the woman he promised to the 'hero' for, saving him out while encouraging him to not give up easily and try his best if he wants to play the the 'hero'.
Idek how to interpret this really. It's just interesting.
To be honest, I vaguely remember the context in which Jessie calls Cloud her hero. Which she does a lot. I wouldn't say it was necessary sarcastic (although Jessie was sarcastic a lot in this game)
Jessie my hero lines. Its kinda a long video.
With Aerith, I think it is a little more difficult to find, I only found once instance.
Aerith My hero lines. I am sure there are more. If anyone else know of more please post them.
With Tifa, I think the only time she mentions hero is during the water tower flash back and the one post earlier.
Now, if we examine Cloud's facial expressions, during the scene at the Shinra building I think you are right about a mutual understanding and Tifa is encouraging him to do better.
Honestly now that I am thinking about it. It could be considered condescending in all honestly. Tifa should know that Cloud is doing the best that he can. I mean he stayed back so the rest can escape! Even though it was totally reckless and I think that is what Tifa was conveying with those lines.
Indeed Interesting thought process here!
edited to correct the last paragraph sentence structure.