Road to Ninja Tsunade Bio:

Tsunade is a reserved, refined woman with a gentle soul. She is strong willed, but is never really rash, or ill tempered. She is somewhat like an auntie, or grandma, when you speak to her, generally. She is very humble regarding her great skills as ninja.

She is very lucky. She was never fond of gambling, but has done so at the request of others due to her amazing luck with it. She currently has one student, Shizune, but has recently become interested in possibly taking another.

Instead of regular Tsunade's fear of blood, she has a fear of bodies that take on lifeless characteristics. Such as a sleeping body that may seem lifeless if it doesn't move enough. This does not really affect her in combat like regular Tsunade's fear would, as it is much different. It is a very mild PTSD from seeing the lifeless bodies of her brother, and deceased boyfriend.

One last thing: Her recognising your character as the version from her world isn't unlikely. If said character's Road to Ninja version hasn't been shown, they will be perceived based on the writer's headcanon. This can also apply to characters not from Naruto, based on my own headcanon. You can choose to go along with it, or not. I often choose to recognize characters for their non-RTN counterparts, as never doing so can get annoying for me.