Hi and welcome to the forum
IMO, even if it is a tutorial and irrespective of how close you want to get to the reader, you should stick to full forms. There are other ways of getting closer to the reader (include pictures, or user-friendly explanations in non-technical terms if needed). Using contracted forms would give me (a non-technician reading the tutorial) a sense of unreliability.
But then again, maybe it's just me. Native speakers or teachers amy have a different (and better-based) opinion.
PS: Imagine writing the same in German. My guess is you would write "Ich habe es schon erklärt", not "Ich hab's schon erklärt".