It depends what you consider "accurate". Basically, you have to consider scan time. If the ladder that include the "start timer" instruction is near the top of the scan and the button is pressed while the bottom of the program is scanned, the program will not detect the input until the next time the inputs are scanned. This may be only a millisecond or two later - it depends on your PLC type, the number & type of instructions in the program, etc. Same thing for detecting the second pushbutton.
Without familiarity with the 830 PLC, I can only assume that their timers are as good as the micrologix, which are generally sufficienct for most tasks.
If the 830 has a "FAST" input function, you can try using it. Some of the Micrologix do. Scan time will be a thing of the past.