I have a hardcopy subsrciption to SI, so the iPad SI app allows me to download their electonic versions for free. So my response is based on that experiance. I do not know what it is like if you've paid for a SI subscription on thru the SI app on your iPad.
I found that the SI app on my iPad shows each issue, but does not automatically update them. When there is an issue I want to have on my iPad, I have to click the "download" button on the issue's cover. I have a WiFi only iPad and get my issues when I am in a WiFi hotspot. Hope this helps some, although I know it does not answer your question about downloading on your computer and then putting it on the iPad.