I will let others explain the particulars. This verb is kind of tricky. So I will approach it from a conversational angle.
Usually, with upload, we use present continuous, or simple future with going to, or depending on the time it happened the simple future or simple past.
I just uploaded or I uploaded some photos onto my computer. I'm uploading some files onto my computer. I'm going to upload some photos onto my computer. I'll upload those photos onto my computer. In American English, you can say, I upload photos onto my computer. But it sounds kind of pretentious to say it that way.
I'm not sure how other countries would differ their usage.
Informally: We may say. I put it (photos) into my computer.
I'm not sure if that is substandard English or not, but we do say it sometimes.