You can't just be like "it's a lovely morning time to...
launch a rocket and put people up in the ISS"
You have to wait for them to be able to meet essentially - you fire this thing off in a direction, make it tilt a bit, then that spirals into the way of the ISS and with a bit of manoeuvring they line up.
Remember you're not trying to intersect with the ISS - you want to move in so your direction and the ISS line up.
You can do this anyway, but you really want that big-ass rocket you discard to do MOST of the work, and the remaining propellant (fuck all, few drops - compared to rocket) to give you a nudge towards it so you do align. This is what corrects the rocket's error in where it went.
As a slight ... brag (I really want to show people who are not students who are automatically in awe of everything) I've been working on like "KSP for adults" (without ever playing KSP) because I was annoyed by the number of students thinking this made them experts (I don't hate students, I hate some of them, especially the ones who are given a grain of knowledge and suddenly know everything - but I'll suppress that rant)
I recently tested it with moon landing (naturally) and Hayabusa 2 - it's going well (this mission mostly worked, I got it to the right place at the right time for a lot of things, bit of a language barrier - but with their mass and propulsion capabilities everything worked! Looking to get more accurate "what they did when" but they keep good English updates so I can infer a lot, like checking remaining reserves line up ect).
Love to share it, it's really coming together.