Not at all!
Angel Watch ships with its own SIM card. It has it's own account.
The plan is month-to-month (no contract) so you can cancel anytime and there's no chance of overage charges.
So with the watch having its own plan with its own number, sufficient minutes (1000), and data (500MB), there's no need for you to change your network personally and calls would just come out of your respective plan's minutes.