From the part of the manga which is past s2 and goes into the movie:
Yotsuba recognises Fuutarou from the start. (See Ch90.) Ichika doesn't. (I think that Ichika doesn't recognise should be inferred from S02E10 or S02E11 or something when Ichika picks up the photo that Itsuki dropped.)
There are 2 aspects to this.
Ichika is friendly nonetheless. I don't see any reason to think Yotsuba is just that good a human being and would've been friendly otherwise. It's arguably part of Yotsuba's being a genki. But of course Yotsuba's genki-ness is arguably kinda fake.
Receptive to tutoring:
As for Yotsuba's being the 1st to be receptive to tutoring, well yeah that's largely because of the promise Yotsuba and Fuutarou made to each other and themselves all those years ago.
Note that Ichika isn't receptive to tutoring until S01E05. Miku is even receptive in S01E02 before Ichika (but after Yotsuba).