True, it is the same type of behavior and she did verbally confirm it instantly. Though, she just cared enough to correct her about the name of her character.
And you are correct on the similar behavior of tsundere.
Also, why is this gender bend/TS, I guess the author just wanted to include it (+ make a cute character). lol
Could've been a regular "I was Isekai'd to war" manga, no need for the TS.