ST01C timer replaces one 3-way switch and the other 3-way switch remains.
The ST01C timer does not work exactly like a 3-way switch.
When the timer blue and red wires are connected together, they reverse whatever program is in effect.
When the timer is wired for single-pole, the red wire is capped off. When timer is wired for 3-way, the red wire is used to reverse the timer, thus causing the 3-way effect.
So if timer is ON, and red and blue wires are put together, the timer turns OFF.
That's why the remaining 3-way switch has to be rewired.
The remaining 3-way switch is rewired so it will connect and disconnect the red and blue wires, causing the timer to reverse program each time, and creating 3-way effect.
Other requirements of ST01C is that the black wire must connect to Hot wire, and the blue wire must always connect to Load. This means that you have to correctly pick which 3-way switch to replace, where the hot wire from breaker arrives.
Open following link for wiring diagram showing how to wire for 3-way:http://waterheatertimer.org/ST01C-program.html#ST01C
All 3-way timers require rewiring second 3-way switch to create 3-way effect.