Not necessarily. If they watched the video but clicked away somewhere near the end, yt will remember that position for them. If they later saw it again on their homepage and thought, “I liked that video, I should share that” then the link they have there is going to include the start at end bit. Lots of people do not know, or care, about all the bits of a URL so OP could have been ignorant to the fact that URL they copied would do that, or simply missed it, or not cared even after noticing. But I find all of these more likely than OP specifically added it, as you say.
Not necessarily. If they watched the video but clicked away somewhere near the end, yt will remember that position for them. If they later saw it again on their homepage and thought, “I liked that video, I should share that” then the link they have there is going to include the start at end bit. Lots of people do not know, or care, about all the bits of a URL so OP could have been ignorant to the fact that URL they copied would do that, or simply missed it, or not cared even after noticing. But I find all of these more likely than OP specifically added it, as you say.