This website explains that:
「~ところへ/に」は、ある段階における状況を変化させるような出来事が起こることを表すと説明した方がいい。
to indicate event that will change the situation in certain stage
(this is my own translation (it might be incorrect))
「~ところで」は、前の動作が終わり、一区切りがついた時点で、後の変化が起きる、又は動作を起こす。
In a point of time when the action is over and there's a break, another action happens / perform another action
(this is my own translation too)
ふっとうしたところへとりにくを入れます。
I think ところで is more suitable (even though I think it's wrong) in this sentence because 「前の動作が終わり、一区切りがついた時点で、後の変化が起きる、又は動作を起こす。」
前の動作が終わり = ふっとうした 後の変化が起きる = 肉を入れます
But anyway, I feel like I don't understand the difference between ところで and ところに/へ at all because when I feel it's unnatural when I use it. See also Usage of ところ to represent time with に and で
It implies that “While the teacher was walking down Shibuya road, I met someone not being mentioned (could be 先生 but I think most people are confused by this kind of phrasing and it’s almost not spoken)” This is my way of thinking of the difference betweenところに/へ andときに right now. How is it ? – Kyuu Jun 19 '20 at 11:03