Instagram recently incorporated the ability for your followers to know if you are online. Here is how to deactivate the function.
Being stalked on social media is not always pleasant. While Instagram is currently testing a function to be alerted when one of your subscribers takes a screenshot, the social network activated a few days ago, a new feature allowing your subscribers to know when you are in line.
Activated by default, this option allows all subscribers with whom you have exchanged messages in private, to know if you are online, or to know the time of your last connection.
To deactivate the function, go to your profile page, then enter the “Options” of the application.

Scroll through the settings, and turn off the “Show online status” option.

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