WordPress Core WordPress auto update

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Core WordPress auto update, by nitishc

My website was managed and hosted on a different service provider initially. Due to to some service issues I moved my website to another host. But I got an auto email from my previous provider that they have updated my website
to a new version of wordpress (4.9.2) and its really got updated.
Do my previous provider still have access to my website ? I do not want these auto upgrades and from previous hosting provider. Please suggest.

Core WordPress auto update