Thanks for this thoughtful question, and apologies for not noticing it sooner.
First of all, just to reassure you a bit, this is definitely a rather subtle point (and the sort of thing that even natives might have some difficulty explaining in a concise manner), so don’t feel too discouraged if it’s not completely clicking at first.
With this particular distinction, I think it may help for you to think in terms of what sort of event or action follows the ところに／ところで.
I’m going to link a page I found in Japanese (intended for native Japanese teachers) that has some good examples and explanations of the differences between these expressions:
(16)マラソンランナーはゴールに到着したところで、倒れてしまった。
(17)林さんに電話をかけようとしたところに、その林さんから電話がかかってきた。
(18)夜道を歩いていたところを、誰かに頭を殴られた。
To summarize what the author of the article is saying in Japanese (though I encourage you to also give a try reading it for yourself), note how (16) sets some kind of scene (by establishing some sort of action or change), and then describes what happened at that point in time, similar to your soccer game example also using ところで.
In contrast, with (17) and your phone example, something or someone is ‘coming into’ (literally or figuratively) that scene or situation (as opposed to something happening within the scene or situation itself). If you think about it a bit abstractly, you can see how this even connects to the more fundamental meaning of に marking a ‘target’ or ‘destination’, in contrast with で which marks a ‘place of action’. (Aside: the author also mentions that ところへ can be used relatively interchangeaby with ところに).
You didn’t mention ところを specifically, but just since it’s another interesting point of contrast and the author of the article covers it, note how the nuance/usage is slightly different here – in this case, what follows in the second half of the sentence is something that acts upon or directly effects the scene or situation itself, another example being:
(19)こっそりたばこを吸っているところを、父に見つかった。
With this and (18), it’s not something happening within the scene (ところで) or something external appearing or arriving in/to the scene (ところに), but rather something affecting or ‘operating on’ the scene as a whole (including the speaker and their actions). Again, if you think abstractly, you can see how this connects to the more fundamental ‘direct object’ usage of を.
TL;DR – to understand the difference between how these (very similar yet subtly distinct) phrases, it’s probably most intuitive to think about what follows the ところ expression, and its relationship to the ‘scene’ as a whole (and consider this in light of the fundamental meanings of the particles で, に, and を).
Apologies for the wall of text, but hope that helps a bit!
