I was reading a local publication in which a job coach was giving people advice on when and how to use employer resources during a job search. My approach is different: Never use an employer-owned computer, tablet, or phone as part of your job search. In many states, including Illinois, an employer can fire you if it learns that you're looking for another job. Does that every happen? Rarely -- but it can happen. More likely, an employer who knows that you're looking for work would make your life miserable and try to make you quit.
What's the solution? Never use an employee-owned device for you job search. Purchase a computer and phone that you can use for private matters. Another reason to do this is ethical. Put yourself in the employer's place: How would you feel if an employee were using your devises and paying for service that lets you look for another employer? A final thing to think about, if you were terminated without notice, what would you do to keep your job search going. You'd have to buy a phone and computer. Start by doing that, and you'll have no worries about what your employer will do.