LinkedIn is introducing a new feature that allows you to see 1st degree connections who are 'live' on LinkedIn when you are. If you don't want people to know when you are on LinkedIn, just go to your privacy settings and turn this new feature off. 

Starting conversations is important to building relationships so seeing that someone you want to message is on LinkedIn when you are could be handy. However, there should be no expectation that your LinkedIn connection will respond just because they are on LinkedIn when you message them. Badgering a connection on LinkedIn will only damage the relationship. 

Use common sense and good manners and this new feature might be useful.