Does iCloud automatically update?

I accidentally added a picture to my photo stream last night. It was something private.iCloud photo stream was open on my computer. I deleted it from my iphone's photo stream immediately and I went upstairs to delete it from the computer but my mom was on it. This picture is something that could get me in a lot of trouble. Would the picture have been deleted off my computer as soon as I deleted it off my iPhone?

It should be deleted as soon as you delete it from iPhone because it keeps syncing

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