Don't forget they can use you, as long as you get your 10 hours rest in the last 24 hours. They can call you for an assignment after you have had your 10 hours of uninterrupted rest and your duty doesn't start until you report to the FBO, which is 1 hour before departure. But you can't take an assignment unless you've had your ten hours uninterrupted rest looking back 24 hours.
That is correct. They can use me after 10 hours of uninterrupted rest providing they put me on duty after 10 hours. I still don't have to answer my phone until I'm on duty. I am not obligated to the company during my rest period no matter how long it may be; 10, 11, 12, or 20 hours. No 135/91k pilot is obligated to the company during your rest period.
Your rest period must be defined. There are only two states a pilot can be placed in; rest or duty. You can't be sorta in rest or sorta on duty. You can either be in rest and free from all duties to the company, or you can be on duty and then they can do what they like with you. If rest and duty are not defined on a daily basis you could fall into the trap that a lot of scum bag operators try to pull. They try to roll the clock back and forth to benefit them. Say you stared your day at 1200z. You then finish your last trip at 2200z. If you do not have a defined release time are you on duty till 0200z or shortly after 2200z? So when does you rest start? When is your required 10 hours of uninterrupted rest begin? Without knowing what your defined rest period is how do you know if you are legal to do that pop-up trip. The reason the feds made the rules was for safety. The reason companies try to bend or interpret the rules in their favor is for profit.