ANSWER - I’d kind of like to park this question and come back to it in thirty years when I’m a wise old crone with fifty odd years of practicing magic under my belt. The reason is that your question tackles the very fundamentals of magic and the complexity of how it actually works and it’s a pretty tricky business.
Magic is an entirely non linear process. This is why people find it so hard to comprehend. In the scientific world of direct cause and effect its easy to dismiss something that works in a completely different way to the laws of the world that we are used to. The best explanation I can give is that the practice of magic isn’t a direct influence of intent on outcome. Magic is endowed with its own interpretation of intent and works in an roundabout meandering route rather than creating a direct influence. As you point out in your question, this makes it very hard indeed to know if something actually is magic or just a coincidence.
The thing is a lot of witches do mistake the two. That eye rolling moment when they assure you they make the traffic lights change colour upon approach (coincidence!) or they receive a cheque out of the blue after practicing absolutely no magic to obtain it and assume it is a result of their powers…. Its easy to take every little happening as meaningful and/or magically generated but the truth is that most of the things that make up 99% of our lives (witch or not), just kind of happen and are not a result of any magic we work.
The first sign that something actually is influenced by magic is forethought and intent. If you know you have worked on something magically and the results you obtain come to fruition, you can have if not a certainty but a credible claim that it may have something to do with the working you have performed. This is backed up by regularity - the more you see results from your magic, the more you can feel confident about making the claim that what you are doing is working. If only 25% of your spells ever work (25% is the luck/coincidence alone figure) then chances are you are having little influence. If however you see a consistent outcome in situations where you have applied tangible magical intent then likely you can start to feel confident that what you are doing is working. Its a bit like that old saying “the proof of the pudding is in the eating” but in this case you need to eat quite a few puddings before you can rely on the fact that what you are doing is actually having an effect.
I'm not entirely sure that it matters too much if you occasionally give yourself credit for something that would have happened anyway. Spellwork, as we know, is all about intent - if your intent becomes strengthened on the back of a few coincidences it can only have a positive effect on your future magic. And vice versa, sometimes we can send out our intent without realising it and influence situations that we did not realise we were trying to influence. So the line between the two remains very blurred but in my own opinion it comes down to consistency – When you can state with confidence what will happen as a result of a spell, fully believe you can control the outcome and ultimately and with regularity obtain the results you desire, that is enough to convince me at least that some magic is being worked.